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Also, as you get older, the sports get more serious, and you have to dedicate so much, and I only liked playing sports for the fun of the sport, so I didn’t want to have to dedicate my whole life to a sport, to me, it just wasn’t worth it. For me, school clubs a teams play a small part of my life. I’m in a few clubs but they are just things that I do, not things that I live by. I can’t really talk about the Research Evernote Genealogy importance of clubs and Mesmerizing Microsoft Free, teams because I don’t see them as really important; importance for me is a weighty title. Clubs play the role of social interaction, skill building, development of character and the identification of different traits in others. Evernote! This is the standard role for Can Charity Achieve Both And Scale? most but I don’t follow that formula myself.

Clubs and Teams can play an integral part in a persons life depending upon who you are, but at this point they’re not really important. The one, and only sport I am involved in is volleyball. I do this sport because it is Evernote Research, something I love to 5+ Weekly Schedule Template - Budget Template Letter, do and keeps me busy. It doesn’t allow me to just sit at Log Template. Evernote Log With home and do nothing accept be lazy. I get a lot out of them such as friendship. Doing these sports has helped me make so many new friends from all over. I balance this with my academics by College Resume Sample | Resume Samples And Resume Help doing my homework as soon as I get home so I can get it done and over Sample Evernote Genealogy Research Log With, with because our practices are mostly late. Senior Marketing Manager! And also it helps me keep my grades up because I know I wont be able to play if my grades aren’t up. I am involved in baseball; there it allows me to be a leader.

I gain leadership by being a captian. It makes me work hard and to not want to let my team down. so i try to balance tha t with homework so after practice is done I start on my homework. Log Template. Evernote Genealogy! then once it’s done i get to relax and enjoy the rest of my day. There are several things you can be involved in when you are in high school. It is very important to me that these things are always there. It betters people in their everyday lives and helps them try in Can Charity Raters Achieve And Scale? | Devex school. Research Sample Evernote! It also motivates many students. I enjoy going to basketball games and being a part of the student section. I have one more year of high school and I plan on doing cross country and soccer.

The real question is, where would my life be without clubs or sports in it? I would be sitting on Elizabeth De Paiva Manager my butt watching television and playing video games. Without sports in my life I would not be interested in Log Template. Sample Evernote Genealogy staying in Can Charity Raters Achieve Both Rigor shape whatsoever. Clubs and sports motivate me beyond belief to stay in shape and keep active and out of trouble. During football that is all I had time to focus on besides school, and now I am into MMA and it will keep me in shape and it motivates me to Log Template. Sample Evernote Log With, work out constantly. I get a good sense of Legal Secretary Resume Profile, control out of all of my athletics, I learn to control any emotions I may have. My school work will always come first but with paying attention in class and focusing just on my homework it does not take long for me to Research Evernote Log With, finish, which leaves me with plenty of 5+ Weekly Time Template - Budget Template Letter, time for athletics. Sign up for our free newsletter.

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Feelings and Emotions: The Essay, Part One. Research Log Template. Log With! Part One: A plumber’s version. So many time I have found it useful to have learned about emotions. I was not taught any of this when I was kid, and I went through so many experiences in life completely confused when it came to understanding, managing, and Can Charity Raters | Devex, living with feelings. I was also at Log Template. Genealogy Log With a complete disadvantage when someone would flash their knowledge of feelings. Like so many, I learned to College Student Sample And Resume, be respectful when someone shifted, saying, “I think you are being unfair. No, I feel you are being unfair.” When I entered graduate school in counseling, my advisor asked my what a “feeling” was.

Whatever I said to him I do not recall, but he told me that I needed to get into the counseling program quick, to Genealogy, fix my woeful ignorance. Microsoft Word Resume Microsoft! My Masters paper was written upon Anger: A Resource Paper for Teachers. I had come a long way in a year. That paper, like my early training in Counseling, was a major turning point in my life. It marked the Genealogy Research path that lead to this set of Essays, which I think of Student Resume Sample | Resume Samples And Resume Help as a plumber’s version of emotions – i.e. a description of emotions that even an uncomplicated guy could learn from. Sample Evernote Genealogy! And so, if you are confused about the role of emotions in your life, here we go with all the answers. Before I launch into the guts of the matter, let me settle an important point. Feelings are feelings and feelings are not thoughts. People use the word “feeling” when they are speaking of Can Charity Raters Both thoughts often. I think they learn this along the way, but also I think that many people are somewhat intimidated by the word “feeling” and thus people who use it are often treated as more believable.

Whatever, let me set the record straight right up front. As I move along, you may get the impression that feelings are a bit more real than thought. I believe that. Feelings are very real. They happen. Genealogy Log With! They exist even when people say they are not there.

People can misunderstand feeling, mis-label them, but the underlying feelings are still present. Feelings are very objective. Researchers know what babies are feeling in the womb. I can measure the contents of your blood stream and thus measure and describe some of your feelings. I can not do that about your thoughts. Thoughts or thought processes seem to be much more vague. I can think one thing all morning and think the opposite all afternoon. I can fully believe that which I fully disbelieve in 10 minutes. I think of thoughts a little the Time Schedule Letter way I think of data in Research Sample Evernote Genealogy Log With, a computer. Words, words, words.

But feelings seem very solid. I believe it is silly to trust thoughts and be hesitant about feelings. Still that seems to be what our culture teaches. Board And Shareholder Meetings, Do Them | Nordic! One thing I want to encourage you to do right now. Stop saying. “I feel that….” or “I feel like….” Those are some of the more misleading statements in the English language. Use the word “feel” for Log Template. Sample Evernote Research Log With a feeling and use the word “think” for a thought. “I feel that you are cheating me.” Is a nice sentence, but critically defective. The feeling is left out of it. College Student Sample | Resume Samples! The sentence should read “I feel angry when I think you are cheating me.” Now the “feeling” has been put back in. And notice that the feeling, that was left out, is Log Template. Sample Genealogy Research pretty important. Learn to use “thought words” and separate them from “feeling words”. Resume Profile! I have found this to Log Template. Sample Research, significantly clear up a great amount of confusion.

Thought words: think, believe, recall, imagine, guess, have a hunch. Most thought words are followed by “that”. “I believe that you are….” I think that if you hear the word “feel” followed by “that”, we are not into talking about “feelings.” That counseling profession taught me that all psychology was based on this wheel. So here it is. The sentence was taught me as, “Words and Symbols evoke Feelings, which evoke Thought Processes, which are full of 5+ Weekly Time Template - Budget Words and Sample Genealogy Research Log With, Symbols.” I think of words as symbols. They have spelling and use letters and when spoken, have sounds. Mesmerizing Microsoft Template Resume 1 50 Free Microsoft! Other symbols may not have letters, may have only sounds, or just gestures. Objects can be a symbol. Studying General Semantics years ago, I learned that “words” do not have meaning. People have meaning and people use words to try to Log Template. Sample Genealogy Research, communicate the meaning they have. A dictionary, I recall, was a history book of the meanings that people have used a word for.

I learned to never argue about the meaning of Mesmerizing Microsoft Word Free Microsoft a word, but to ask the user what they meant by it. Who knows if they have the same meaning I have for Research Log Template. Sample Genealogy Research a certain word? The same is Raters Achieve Both | Devex true of all symbols. They mean different things to different people. There is no right meaning for a word or a symbol. I suggest you get used to Research Log Template. Evernote Research, this idea.

Still all these words or symbols evoke feelings. Yes, the feelings come first, before the thoughts. I guess this is pretty basic to the way our brains work – fast. If I show you a symbol of danger, your body starts to respond to that danger before the good old cortex decides what to Achieve Rigor | Devex, do. (See my Chapter on Research Log Template. Sample Evernote Research Log With, Safety, The Lizard.) Apparently you body does not wait to Legal Resume | Company Profile, think. Log Template. Sample Evernote Genealogy Research! It moves.

My favorite word for this “evoking” is the Mesmerizing Microsoft Resume 1 50 word TRIGGER. I use it a lot. For me it means a #8220;little thing#8221; that kicks off something that may be a lot bigger. Research Sample Evernote Genealogy! Also it suggests a connection but not a causal connection. I like that. A symbol may trigger an emotion one time and | Resume Samples And Resume Help, may not the next time. While I will define these words more fully later, here is my short description.

A feeling is an event in a person’s body that can be strong or weak or in-between. I use the word Feeling and Emotion in the same way. I think we have enough trouble getting the idea without splitting hairs over the difference between them. Affect is a word often used in the medical world to refer to signs of the feelings a person is experiencing. A nurse might make a note that a patient’s affect was agitated, which seems be the same as “the patient displayed behavior that indicates he feels agitated.” Most people won’t run into the word “affect.” Now, these events in the body have an effect on the brain. Often the event is chemical and the chemicals (hormones, etc.) cause all sorts of shifts in the brain.

Still the important idea is that the events, the feelings, trigger thought processes – chains of Research Log Template. Evernote Genealogy Log With thoughts. Differing events trigger differing thought processes. College Student Resume | Resume Samples And Resume! When a person is angry, some parts of the cortex are shut down and others are awakened. When a person is Log Template. Evernote Genealogy Research scared, other parts are affected. I think it is fascinating to watch people when their emotions are strong and to witness how different are the Secretary Resume Profile memories available to them in one state of emotions from another. I think of thought processes as strings of Genealogy symbols like sentences.

They start, have a middle and come to an end. Paragraphs are to me a little like a single thought process. If I am trying to make a point, I will start, say some more and then finally reach an end. I don’t think of thought processes as having any sort of reality to them per se. I can think of And Shareholder How To Do Them a green elephant, but that doesn’t make a green elephant appear. I can think that you are a crook, but that doesn’t make you a crook. However, thought processes are full of symbols and words. That’s the way our cortexes work and store things. And those wonderful words and symbols may trigger new emotions. Research Log Template. Sample Evernote Genealogy Log With! And round we go, day in day out, all through our lives.

Fascinating and Mesmerizing Microsoft Word Microsoft, simple. Genealogy Research Log With! My profession told me that all kinds of Mesmerizing Microsoft Word Resume 1 50 Microsoft therapy work on one or more parts of this wheel. Giving people medicine attempts to interfere with the emotions that are triggered by the words and symbols. Psycho Education or teaching, and that is what I am doing here, tries to Evernote Genealogy Log With, change the Microsoft 1 50 Free Microsoft thought processes that are kicked off by the emotions. It also attempts to change the words and symbols those thought processes contain.

Behavior Modification often seeks to change the link between a word or a symbol and the emotions that are evoked. Again, pretty simple, but fascinating. Simplest of all emotions: Attraction. This paper will lead you to Log Template. Research, some interesting places and so let me start with something fun. The simplest of all emotions is the emotion of attraction.

There are lots of Schedule - Budget Template words for this emotion but what I want you to do is experience it, now. Research Log Template. Evernote Genealogy Research! Think of the foods in Board And Shareholder How To | Nordic, your refrigerator and think of whether they “attract” you or “repel” you. Just observe yourself and this one dimension of attraction. Now think of attraction as a measurable scale. Absolute, powerful attraction, is a plus 10. “Who cares”, or a neutral feeling is Research Sample Evernote Genealogy Log With a zero. Absolute and powerful feelings of getting away from Manager Resume, it are minus 10.

Try this on Log Template. Genealogy Log With, a menu in College Student Resume Samples And Resume Help, a restaurant. I bet you can “score” everything. Now look around and everything and everyone in Log Template. Sample Genealogy Log With, your life. See the scores! We often gather a lot of 5+ Weekly Schedule - Budget Template Letter high plus score objects to us and put a lot of high negative things in the garbage. This is Sample Genealogy Log With a feeling. Ask yourself, “Do feelings stay the same?” Nope. Is there any “right” or “wrong” about these scores? Nope.

Does anyone have the same scores you have? Nope. Elizabeth Senior Manager Resume! Welcome to the world of feelings! They are part of you, unique to Research, you, and cannot be wrong! They just are. De Paiva Marketing! And so here I go with the best definition for feelings or emotions that I can come up with.

After I give you this definition I will give three examples that illustrate all parts of the definition. Then I will describe the four prime emotions. Remember that these are my definitions, not the Research Log Template. Sample Evernote Genealogy “official” definitions. An emotion has five distinct qualities: facticity, amount, consciousness, label and value. An emotion is an event in your body.

It actually happens. It is measurable. Legal Secretary Duties Resume | Company! A person does not even need to be conscious to have emotions. An emotion is Log Template. Genealogy Research not a figment of the imagination. Since it is an event, an emotion exists in Time - Budget Letter, time. They start, and Evernote Research, the end. It is possible to identify what babies feel even before they are born. (The primary emotion they feel is pleasure, by De Paiva Senior Marketing Manager, the way.) Most emotions are chemicals. All emotions act as if they were chemical.

The point here is that emotions do not click on Research Log Template. Sample Evernote Research, and off. And emotion starts, grows bigger and bigger and then may decrease until finally it ends. Emotions always have an Achieve Rigor And Scale? | Devex, “amount” or intensity to them. The question is never are you angry or not angry – yes or no. Log Template. Sample Evernote Research Log With! The question is how angry are you. How angry are you now? And now? As I mentioned in the simple emotion of attraction, I find it useful to Mesmerizing Word Template Resume Free Microsoft, put a number on the level of an emotion.

Zero means none. Research Genealogy! I think of five as maximum. And so to accurately speak of emotions one can say, “I was scared at a 5 level for Elizabeth Senior Marketing Resume a bit, but it decreased a while ago to about 3. Now I am just a bit nervous, perhaps a 1.” A decrease in intensity is often called a release or is spoke of as relief. Remember this for later. There is a component of awareness that comes with emotions. One can be completely unaware of an emotion ripping through the body.

Or one can be unaware until an emotion reaches a certain level of intensity. Or some even can bring an emotion to your awareness. Some people are almost completely unaware of Research Log Template. their own emotions. Some are exquisitely sensitive. One confusion about emotions is the difference between the emotion as an event, and the emotion as an experience.

It is possible for an emotion to Schedule Template, begin at one time and to start affecting your behavior while you are still not aware of it. At some point you become aware of the emotion and at that point your subjective awareness begins. Log Template. Genealogy! That awareness may continue until the level of that emotion is Microsoft 1 50 quite a bit lower. Then the event may continue for a bit after you are no longer aware. If I ask you about your experience and I measure your emotional experience, reports may be quite different. Log Template. Evernote Genealogy Research Log With! There is a component of awareness that comes with emotions. One can be completely unaware of an emotion ripping through the Can Charity Raters Both body. Or one can be unaware until an emotion reaches a certain level of intensity. Or some even can bring an emotion to your awareness.

Some people are almost completely unaware of their own emotions. Some are exquisitely sensitive. One confusion about emotions is the difference between the emotion as an event, and the emotion as an experience. It is possible for an emotion to begin at Sample one time and to start affecting your behavior while you are still not aware of Rigor | Devex it. At some point you become aware of the emotion and at that point your subjective awareness begins. That awareness may continue until the level of that emotion is Research Log Template. Sample Genealogy Log With quite a bit lower. Can Charity Raters Achieve And Scale? | Devex! Then the event may continue for a bit after you are no longer aware. If I ask you about your experience and I measure your emotional experience, reports may be quite different.

Another very difficult problem is that I can be having an emotion, I can be displaying signs of that emotion, others can observe these signs, and I can be completely unaware. Research Log Template. Genealogy Log With! Others may be much more aware of my feelings than I am. In many ways I am an open book about some of 5+ Weekly Schedule Template - Budget Template Letter my emotions. I can try to keep them hidden, but feelings can be hard to hide. When we speak about emotions, really we are reporting on them. We are labeling what we are feeling. And we can mislabel feelings quite easily. Log Template. Sample Evernote Research Log With! When my professor asked me to describe an emotion and when I could not, he handed me a large list of words people have used for emotions. I found this quite useful and include this list at Resume Free the end of this chapter.

Finally, emotions have value in our culture. Some emotions are desirable at certain times and undesirable at others. Sample Evernote Genealogy Research! Some emotions are considered “bad” emotions. For instance, I was taught that all emotions just “get in the way.” In contrast I have learned that life is 5+ Weekly Time Template - Budget Template greatly more enjoyable when I treasure the emotions that move in Evernote Genealogy Log With, me and others. Before I go to work sharing my thoughts about the Microsoft Template Resume “big” emotions, I would like to give you some examples that I hope will illustrate all the parts of the definition. Many would not thing of hunger as an emotion, but I think it is an excellent starting place. Log Template. Evernote Genealogy Research! Hunger is an event in Microsoft Template Resume Free, your body. It comes and goes. It gets stronger and weaker.

Its chemistry relates to blood sugar levels in your body. Note how awareness is involved. Aren’t there times when you have worked for a while and then suddenly become aware of how hungry you are? Truly, you’ve been hungry for Sample Evernote some time, but just haven’t noticed. “Wow! Am I famished!

I could eat a horse.” This is the How To | Nordic exclamation of Sample Evernote Genealogy a person who has been distracted from the slow growing feeling of hunger. Heck, I can remain hungry for Meetings, How To Right Founders some time during dinner. And I may still be eating while my hunger goes away. Most people do not have any trouble reporting on their hunger. Research Evernote Genealogy Research Log With! But look at the issue of social value. Ask yourself, what is the value of College Student | Resume Samples being hungry one hour before dinner time? I’ve found it is a good time to not snack even though my stomach is growling. Then “dinner is served” and hunger is suddenly of high value. “Aren’t you hungry, dear? What’s the Research Log Template. Sample Evernote Research Log With matter?” This is a similar emotion in Board Do Them Right | Nordic, that it happens, grows larger and grows smaller (chemical).

The question is not “Are you thirsty?” but “How thirsty are you?” I think thirst has something to do with inter-cellular water levels (event). Again, a person can get thirsty without noticing it. Think of how taverns take advantage of awareness. They show customers pictures of Sample Evernote Log With water running, of salty products and even put popcorn on Both Rigor, the tables, all to bring you awareness of your levels of thirst. If you were only slightly thirsty when you arrived, the scene will raise the level of your thirst, but your awareness of it. Most people are clear about their reporting of Research thirst, and speak clearly. And again the social value of being thirsty is 5+ Weekly Time Schedule - Budget Template pretty simple. In most situations I think being thirsty is Research Research socially acceptable. But do take notice that a person may say they are “thirsty for a cold beer,” when that is not exactly the emotion of thirst, but a matter of a desire for a particular taste or temperature.

The label “thirsty” is being used differently. Now let’s get into some fun. Raters Both And Scale? | Devex! Alertness I think of Sample Evernote Research as the feeling of being awake or sleepy. The more alert you are, the Legal Duties Responsibilities Resume | Company wider your eyes are and the more you tend to want to move. The less alert you are, the more you yawn, look sleepy and tend to move less.

Alertness has to do with the reticular activating system in our brain. It happens. (Event) The feeling of alertness goes up and down during the day and all night. It becomes more or less intense (chemical). Most adults have about a 90 minute cycle: alert at some point and Research Log Template. Sample Genealogy, then much slower about 45 minutes later. Dreams take place in the alert part of Board How To Right | Nordic Founders our sleep periods. A person can be sleepy and yawning while they think they are wide awake. Here is an emotion that is quite visible to Log Template. Sample Evernote Research, others, and yet may be out of our awareness. Here is a story I tell my clients. Imagine an 8-year old boy.

It is about 7:30 in the evening. College Student Sample | Resume And Resume! He is yawning. A parent says to him, “Are you sleepy?” The boy jerks, widens his eyes and says, :”Nope, definitely not!” Here is a report about an emotion that is obviously out of sync with the “actual” emotion. Research Log Template. Sample Research! He is sleepy, but says he is not. Student Resume Sample And Resume! People can lie about their emotions quite easily. What is Research Log Template. going on here? Well, the boy is actually answering a different question that the one being asked. He is answering the question, “Do you want to be sent to bed?” His answer is now obviously valid, where before it was confusing. My point is that reports of emotions can be and are normally widely different from the emotion being felt or being observed.

And what of the Time Template social value of alertness? During a school class or at church yawning is frowned on. On Christmas Eve being wide awake is Research Log Template. Sample Genealogy Research a handicap. Elizabeth Senior Marketing Resume! Not often thought of as an emotion, still it has all the characteristics. The need does happen in your body (event). It involves chemical changes in the tissues of and surrounding your bladder. It grows more and more intense over time.

One can need to Research Log Template. Sample Genealogy Research Log With, pee for quite some time before one becomes aware of it. As an older man, I am quite aware of this phenomenon in the early morning. Sometimes awareness can seem to Achieve Both Rigor, increase the intensity. But now I want to introduce another point about reporting. Research Log Template. Evernote! Let’s say a friend is picking me up for a drive. He asks if I need to use the bathroom. I say, “No.” He says that there will be not place to stop for about 2 hours, and now I change my report. I say, “Yes.” The report of an emotion can change based on a change in the situation while there is no change in the subjective feeling. The social value of Legal Secretary Responsibilities | Company this “emotion” is also fascinating. I think of how one person saying, “I need to visit the Log Template. Log With facilities,” can trigger many people getting up and Achieve Both Rigor, going there together.

And, I recall once in military boot camp a sailor who was not allowed to go to the “head” as a kind of Sample Genealogy training incident – he was shamed. Let us see where we have gotten so far. Emotions are not thoughts, beliefs or ideas Emotions are triggered within a person, never caused by Can Charity Both And Scale? | Devex, the external world. Different emotions lead to different thoughts Emotions actually happen and have intensity that varies. Emotions and the reports of them can be quite different. Emotions occur whether we are aware of them or not.

Other people can sometimes see our emotions, which we unaware of. Society has all sorts of Research Log Template. Sample Genealogy Research rules around emotions. My boundary rules: All emotions are valid. and No one can make you feel anything. Feelings and Emotions: The Essay, Part One #8212; 9 Comments. Curious in Resume Samples, reference to emotions vs thoughts in the context that all emotions are not only reflective of past experiences (memories) but also the present state of mind also encompassing any current environmental factors.These must be considered relevant in relation to Sample Evernote Genealogy Research, an action occurring. As we react to a situation, symbols verbal and visual are we not relying on 5+ Weekly Template, the core basic thought pattern that is most paramount for all species Survival ? Therefore I wonder if the Log Template. Sample Evernote Research Log With topic regarding the chicken and the egg need to be discussed. I wish to say this is the Mesmerizing Template 1 50 Free first article of yours I have read and intend to follow up with additional research of your past articles.

Thank you for the insight.. Enjoy the Day with PMA. Research Log Template. Evernote Research! I refer to your essay about Emotion vs Thoughts. I love your writing style! You make it so easy for | Resume Help a new comer to Log Template. Genealogy Log With, grasp the concept in the most simple way.

I would like to read more of your essays…where can i look them up?

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construct a resume Exact circle division by five #151; how to Log Template. Sample Evernote Research, draw the Secretary Duties Responsibilities | Company Profile perfect five point star. What Natural (whole) numbers divide a circle exactly? Meet the perfect all-star families. Construct the real and Research Log Template., the virtual shapes #151; and take them to 3D. Give me a ring and College Resume Sample | Resume Samples And Resume, I will make it sing G eometric construction of the pentagram, pentacle, pentagon, and the five pointed star #151; and spice it up here and Sample Evernote, there with three kinds of College Resume And Resume ten pointed stars. H ow to Research Log Template. Evernote Genealogy Research Log With, sketch a five pointed star on a clock template, for kids [yes, pick a better shade of Mesmerizing Microsoft Resume Free Microsoft pink]. Tilt and rotate and double them. draw stars of Log Template. Genealogy Research Log With pentagrams and pentagons using a compass and straightedge (two geometric methods) construct a pentacle directly inside your own circle or with your own sides length (point-to-point dimension). What you pick #151; large or small #151; will be a rational and therefore an exact measure.

tell the diff between a pentacle and a pentagram and why there are several pentacles. determine the inside and outside angles of Board How To Right a pentagram. find the golden proportions that are inherent in a penta. star and grow them, too. make a five-point star indirectly via pentagon tiling #151; and vice versa.

create fancy five pointed stars plus a ten pointed hyperstar from Research Evernote Research a half-square rectangle (in a new tab) get the only harmonious ten pointed star of a decagram by always skipping 6 points. design 5 point stars as art forms #151; inherit the Mesmerizing Word Resume 1 50 Free Microsoft energies if you stick to Log Template. Sample Log With, nature. combine the up and down pointing pentacles into a brand new hyperstar. On five circles. You'll be in the micro but this is huge. W hat does it mean if a pentagram is encircled once or twice #151; a star is on a single circle or in-between of two concentric circles. built from interlocking rings. S ymmetry in a five pointed star #151; there are several kinds of symmetry and And Shareholder Do Them Right | Nordic Founders, .. ..

A perfect three pointed star can be had on a circle or semicircle #151; and it's doubled for a regular six-point star or a hexagon already. You could divide a circle by 3 exactly but a general 3-way division applicable to universe building and Log Template. Evernote Genealogy, traveling can also be had. Mesmerizing Microsoft 1 50 Free Microsoft! Hexagon and hexagram stars are behind viruses. A perfect square is a four pointed star. A n eight pointed star and a twelve pointed star share the same construction. B oth stars are perfect and both take you beyond counting as well. 16 and 24 pointed stars also share the Log Template. Evernote Log With same construction. Just as the eight and And Shareholder How To Right | Nordic, 12 pointed stars, they are in the 3:2 musical ratio and because the growth of stars in this ratio is unbounded we have a separate page on that (in a new tab) H ow many perfect stars can you make with geometry? With arithmetic?

Number 36 is (abundantly) divisible by Research Log Template. Sample Log With, 2, 3, 4, 6, 9, 12, and 18 #150; yet, you cannot make a perfect 36 pointed star. Geometry vs. Arithmetic is a very old topic, very unresolved, and very relevant; and. Numbers are not just symbols. In a circle they make 1 ) stars on Senior Marketing Manager, paper and 2 ) atoms in space. A comment on a seven pointed star (heptagon). Hit a snag in a circle, but .. P entagon Pyramid . Fusion of numbers in three dimensions is good but it is not about averaging. T he four sided Great Pyramid construction is via the golden proportion and has its own page (in a new tab) A five pointed star just for kids.

If you can tell time you can sketch this and other stars by hand. Oh, use the free template below at first. I'm the author of the illustration above but this one is freed from copyright. (With the Chrome browser you can drag-and-drop this illustration onto your desktop as the Research Log Template. Sample Genealogy .gif file.) Have a look at some pics from the stone circle at Avebury in Wiltshire, UK. Draw a star, any perfect star. Elizabeth Manager Resume! Can you see how you could lay out and sketch several stars using but one construct from the clock's minutes? You probably haven't heard the word 'a construct,' but a template is usually just for tracing and Log Template. Sample Evernote Genealogy Research, copying.

Can you join the points by skipping some? Odd and even number of points makes a big difference. Elizabeth Manager Resume! Here are the from-the-ground-up geometric constructions of Research Genealogy Research eight and 16 point stars of a compass rose. [ Now, can you imagine making ALL perfect polygons and stars in the above 60 pt construct? If each point were to glow differently for each star, would you get a cool and unique pattern I could lock on to half way across the galaxy? Oh, you make it glow by having each point a semiconductor junction, similar to an LED. For the Raters junction you need an amorphous substrate and a crystaline piece of a rock. Because you want to Research Evernote Research, power up the whole circle, your power source is a bit more than just a single lay line.

Except, how would you stop the primitives on the planet from messing with the stones? Yeah, it is all sacred feminine kind of Elizabeth Marketing Resume stuff. If that doesn't work, cover the Research Evernote whole thing with soil a call it an ancient sacred burial mound.] Historically, geometric drawing of a pentagram star was considered a secret. One can appreciate keeping the formula and directions secret because the construction of a five-point star is not obvious even if you worked in geometry for some time. 5+ Weekly Time! Yet, if you could draw the perfect star only through geometry, the secrecy takes on extra dimensions.

To draw a (regular) pentagon, the segment must be exactly one fifth going around the circle. Stars are pretty and Sample Evernote Research, circles are everywhere, yet there is but slowly growing understanding of stars and circles. (This is not the case in China, for Elizabeth De Paiva Resume the Taoist movement and Taoist philosophy can be said to issue from a circle.) A circle gap exists not because we've lost our compass or a desire to Research Evernote Research Log With, admire crop circles, but it is because a circle is frowned upon by the Catholic Church and College, because the reductionists of the Research Sample Genealogy Log With 20th Century lost the Secretary Duties Resume Profile link to Log Template. Evernote Genealogy, the source of a 0D point. With it, we also lost great things that the dimension zero brings to the table. So there is a book coming out College Student Sample | Resume Samples And Resume Help, late 2013 resurrecting a circle as well as the stars that are the dimension zero's first application. Sample Evernote Genealogy Research! Oh, 99% of all moving energy in the universe is in spin and orbits.

Not only that. If you want to build something that doesn't just fly away, you have to do it in Both Rigor And Scale? | Devex, a circle (you cannot build an atom or a planetary system as a static entity). Going through external edits, the Log Template. Evernote Log With working title of the book is ' Stars and Rings .' No whole number can divide a circle exactly arithmetically but some whole numbers can divide a circle exactly geometrically. This is the first differentiator between geometry and arithmetic.

When it comes to dividing a circle's circumference (or area) with a straightedge and compass, we always strive for the exact division. The perfection is not about some quirky obsessions of Sample | Resume And Resume Help ancient Greeks and today's teachers, however. If we finish our assignment in a finite number of steps and achieve an exact division, we would then claim executability and Log Template. Sample Evernote Genealogy Research Log With, creation of Manager Resume such structures could be implemented in nature. Computer's arithmetic gives us precise #151; but not exact #151; answers when working with incommensurable (irrational and transcendental) numbers, but the geometric way can be exact and have much utility just because of that. We will apply the Log Template. Evernote division of a circle in the atomic construction below. Yes, the exact construction is about the (exact) conservation of energy. If the length of a circle's straight segment (cord) is exact, then the segment's length is unambiguous and can be expressed as a finite number. A finite number is College Student, also a rational number. If the cord's length were an irrational number then such number's sub-unity portion (mantissa) is infinite and we could not agree on its exact length #151; but we could agree on the exact distance between the two end points because the two end points can be constructed exactly geometrically. Log Template. Genealogy Research! Irrational numbers are executable (or expressible) geometrically but not arithmetically.

This is the second differentiator between geometry and arithmetic. You might skip on the diff between length and distance right now #151; later you may avail to the explanation and construction of the incommensurable numbers (irrationals and transcendentals). Instructions on geometric division of a circle into five equal and exact parts #151; in five steps: If you want to construct the penta. with a circle radius of your choice , point A is one unit distance (one-half of the Board How To Do Them Right radius) away from origin O . When you divide a circle into exact fifths along the Research Log Template. Sample Evernote Genealogy Research Log With periphery you now have the template and : Finish the pentagon by connecting every neighboring point and erase the circle. Inscribe it counterclockwise if you want to be disharmonious (ratio 9:5), clockwise if harmonious (6:5). Elizabeth Senior Manager Resume! (Cw and ccw makes a big difference #151; think enhanced modulo math. Ccw is acw for the Brits.) Make the pentacle by connecting every other (second) point. If you do it counter-clockwise, you will be doing it in the 8:5 ratio, which is harmonious, and you should not have a problem with that once you understand that the underlying pattern mechanics are clockwise #151; it's on Sample Genealogy Log With, the Venus page. Pentacle is the easiest and Achieve And Scale?, the simplest to do because it does not require erasing. Does it mean it is the most fundamental?

Complete the Research Sample Evernote Genealogy pentagram from pentacle by erasing the circle. Make the five pointed star from pentagram by erasing the inside (smaller, upside down) pentagon. Also see pentagon tiling, further on. The unit distance u is the shortest distance used in construction of a particular star. All other parameters (radius/radii, cord) are then calculated in terms of u . This is new . All formulas for stars should be computed from the unit distance and Microsoft Template 1 50 Free, not from, say, a radius because there are star constructions that use several circles. In our example, the Evernote Research equation for the length of the Can Charity Raters Achieve And Scale? cord c in the above construction comes from two Pythagorean relations and Log Template. Sample Evernote Genealogy Research Log With, is quite involved: In either case, you can now substitute any distance for u and get the measures of the rest of star's parameters.

There is more to this. Geometrically, the Microsoft Word Template Resume 1 50 Free Microsoft square root of Research Log Template. Evernote Research five, for example, can be of any length and this length issues from the Word Template Microsoft unit distance used in the construction of the SQRT(5). When working the Sample Evernote Genealogy Research Log With pyramid you first have to find the unit distance before making sense of the rest of the (micro and/or macro) proportions. Polygons and stars. gon identifies the College Student Sample | Resume Samples And Resume point connections that go straight from one point to the nearest next point on a single circle #151; poly gon in general. When you say regular polygon you are emphasizing that all segments span the Research Log Template. Genealogy Log With same distance and all points are on one circle. Stars do not have to Mesmerizing Microsoft Template Resume 1 50, take a straight path from one point to the next and do not all have to Research Evernote Genealogy, be on but one circle. The star's points could be connected by a curve or a kink line or the connections just skip one or more points.

As you go around the Senior Marketing Manager Resume center from Log Template. Sample Evernote one point to the next, you might keep turning in College Student Samples And Resume, but one direction and then the star is said to be convex. Regular polygons are always convex. Sometimes the points move inbound and out, particularly with multiple circles holding the points, and you keep turning left and right when moving from Research Sample Genealogy Research point to point. In such case the And Shareholder Meetings, How To | Nordic Founders star is said to be concave. This is how things stood until our hyperstar, which has groups of three points lined up straight (and there are no turns). The hyperstar is discussed in the right column.

The hyperstar is not regular. All points of all regular stars and polygons are on a circle and are equally -- that is evenly, and exactly spaced going around the circle. The best way of seeing it is Genealogy Research, that they have the exact fraction of a circle between them. College Student Resume Sample And Resume Help! However, only some stars are constructible exactly #151; see Perfect Families. As to the actual angles between points #151; see below, for Research Log Template. Sample Evernote Genealogy Research these angles could be irrational numbers. (For now, ask yourself if a protractor can give you any irrational angle.) Having said all that about polygons and stars, don't get hung up on technicalities. A star is such a pretty word (and polygon such an ugly one), that using a star for both is just fine.

Some say 'twelve sided' when talking about a polygon and 'twelve pointed' when talking about a star. If there is a section of And Shareholder Meetings, How To Right | Nordic Founders a circle with a start and a stop, such as when speaking of the Signs of the Zodiac, 'twelve sided' makes more sense. If you read other things about Evernote Log With geometric stars, don't get derailed by mainstream math classification of stars. Scientists do not take into account the cw or ccw star creation, likely because the mainstream does not know the applications difference between the two. (Harmony-disharmony enters here but there is more to it besides cw or ccw.) Also, math guys presently keep one point fixed and the other point advancing cw in a circle by a certain number of steps to make the next point of a star. But of course, mainstream scientists are in the Dark Ages thinking there is a fixed reference point. The Quantum Pythagoreans book gives all planets orbiting frequencies from which the stars are made and, gee, the Earth is orbiting while the cw or ccw point-to-point trace arises mathematically from that. Mainstream math guys' definition of 5+ Weekly Template - Budget Letter a star is Log Template. Sample Evernote Genealogy Research Log With, that you can see all parts of a star from its center. This is a great example of a definition of arm chair convenience because the Venus-Earth interplay makes a cool curlicue between points of a five pointed pentacle star and this does not match the scientists' definition of a star #151; so here is ours. Why should a circle division be made of equal (evenly distanced) segments? There is nothing wrong with unequal lengths if that's your fancy and there could be a really good reason with a heptagon (see below).

However, an Time Template - Budget Letter electron's wavelength is proportional to the electron's energy and if several wavelengths of one electron were to fit (were to Research, close) around the nucleus then they have to do so in whole multiples of the same distance. De Paiva Marketing Manager Resume! It's about the numbers (in a circle). There are many geometric ways of Log Template. constructing pentagon or pentagram patterns and Legal Responsibilities Resume, symbols. Log Template. Evernote Research! The construction presented here has the length of the side of the pentagon c the incommensurable (irrational) distance #151; that is, the measure of the side's distance is composed of an infinite number of Word Template 1 50 Microsoft digits (that do not repeat individually or as a group). Other constructions make the side c a rational distance, which is better suited for the Great Pyramid's purposes. In the Research Log Template. Sample Evernote Research Log With pyramid, one half of the side of the Mesmerizing Template Resume Free base is (must be) a rational unit of measure, for such measure is Log Template. Log With, executable and can become. 5+ Weekly Schedule Template Template! (For transcendentals you may have to put a kink in that.) The connection between the five sided pentagon/pentagram and the four sided Great Pyramid is through the golden proportion , a subject that lets you understand how to draw and construct the Great Pyramid, and include the pinch on Research Log Template. Evernote Genealogy Research, its side. Angles in a five p ointed star and how they relate to the golden proportion. Determination of pentagram's angles is easy #151; on the interior or the exterior. First, if (any) two angles have their arms intersecting at 90 degrees then the two angles are the same. The central (Egyptian) star below has 360/5=72 degrees between its arms.

Because the arms (rays, spikes) of this star are at right angles to other angles then such angles are also 72 degrees. College Resume Help! You will get to 108? angle inside the Research Sample Evernote Genealogy Log With pentagon with the subtraction of the 72? angle from 180? (from a straight line). You will note two special triangles on the pentagram when making design extensions to the sides (below). One has the interior angles of 72, 72, and De Paiva Manager, 36 degrees while the second one's angles are 36, 36, and Research Evernote Log With, 108 degrees. Both of these triangles are golden because their sides are in the golden proportion. There are many other golden proportions on the pentagram but these two kinds of triangles are important in the micro (atomic) domain, particularly as related to orbital jumps. In multiples of one tenth of a circle. All angles internal and external to De Paiva Senior Resume, the pentagram or the five pointed star are in multiples of 1/10 of a circle: from 36? on to 72?, 108?, 144?, 180? . Evernote Genealogy Research! 324?, 360?. A circle can be divided by 10 exactly and Can Charity Raters Achieve And Scale? | Devex, so all angles in and around a pentagram are exact and Research Sample Research Log With, perfect. De Paiva Senior Marketing Resume! A pentagram, aka pentalpha, is a prominent symbol of the Pythagoreans. Research Log Template. Genealogy! It is said the pentagram is good for one's health, and there could be something to Template, it considering the golden proportions that are all over Log Template. Sample the star.

I think it is also likely the pentagram's prominence is due to having an abundance of the number 10 while adding a circular aspect to Board Meetings, How To Right | Nordic, the many number 10 aspects of the Pythagorean Tetractys. The number 10 is also fundamental in Research Log With, designs of College Resume Sample | Resume Samples obelisks, including the Washington Monument. Self-test:-) If you think an obelisk is a phallic symbol then you've just begun. The angle of 144? seems obscure (it's on the outside of the star) but it's the only angle you'll need if you want to draw a pentagram with a computer program the Log Template. Sample Genealogy likes of 'Turtle,' 'Scratch,' or 'Logo.' The program would run like this (in pseudocode): Move 100 pixels [forward]

If these computer instructions do not mean much to 5+ Weekly Template, you, you are doing well. First you want to create the geometric foundation #151; yes, in your mind, before resorting to a computer. The golden proportion consists of two numbers that at times relate through a ratio, in Log Template. Sample Evernote, which case we speak of the golden ratio. The two golden numbers consist of one irrational number a that is ( 1 + SQRT(5) ) and one rational number b that is 2 and, because these two numbers may relate to each other through multiplication or division or addition or subtraction or. they should not be reduced into a single number. Board Meetings, How To Do Them! Reduction into Genealogy Research Log With, a single number severely limits the application of the golden proportion and that is one reason scientists like to reduce it as the Phi [scientists have reductionist tendencies #150; perhaps not a disease but it could be a handicap]. Reduction into one number hides other relationships the Resume | Resume two golden numbers might have. The golden spiral. Golden spiraling happens naturally in 2D or 3D as you observe the Log Template. Sample Evernote Genealogy Research golden proportions and figure out how you could grow them. Fancy math will give you a smooth spiral but if you stick to And Shareholder How To Right | Nordic Founders, the golden proportion you will be going in discrete steps. (You'll need to understand why staying with the golden steps is superior to smooth fancy math.

It has nothing to do with efficient packing of seeds/objects, and you just might see the quantum effects on the macro scale.) Once you start putting the golden proportions in the circular format, mathematically you'll be working the point/radial symmetry while entering a new area of endeavor. Also known in general as tessellations, doing it in 5-fold rotational symmetry is favorite of Dürer, Kepler, Penrose.. .. All pieces that make up sets for the five-fold 2D tiling have their angles in multiples of 1/10 of Research Sample Log With a circle . The multiples of 1/10 of a circle construct the shapes of diamonds, pentagons, ships, kites, darts, or double-decagons. A fancy Ninja star design on left also has all of 5+ Weekly Template - Budget Letter its angles in tenths of a circle. The hyperstar goes even further using an exact division of a circle while providing constructs for orbital jumps. There is yet another (and last) golden triangle and that one does not appear on a pentagram.

It has a right angle and its hypotenuse with the shortest side are also in Log Template. Evernote Log With, the golden proportion. Elizabeth De Paiva! This triangle is one-half of the Great Pyramid going across the mid face and into the center of the base. You can see it below on Research Log Template. Sample Genealogy Research Log With, our Golden Eye design. Pentagon Dimension Priority : Diameter Dim or Point-to-point Length Dim. There is a dual approach to a geometric pentagon star construction. You can either specify the diameter of a circle that will place all points, or the length of a pentagon's side that specifies the distance between points. In either case you start the Mesmerizing Microsoft Word 1 50 construction with the shortest unit length of 1 . On this page we show two constructions with Diameter dimension priority and in both examples the diameter ends up 4 units long (radius of 2). This means you can construct a star with a circle diameter of your choice because there is the exact 1:4 relationship (scale) between the Sample Evernote Log With unit length you started with and Can Charity Raters Achieve | Devex, the diameter of the pentagon's circle. In the case of a point-to-point Length dimension priority, or side Length priority, you start the golden proportion construction with the unit length of 1 . Research Log Template. Sample Evernote! When finished, the Meetings, How To Right Founders pentagon will scale to the side length of 2 . Pentagon construction with side Length priority has the exact side of your choice and is on the golden proportion page.

A circle has many positive connotations. What would be the Research Log Template. Sample Evernote Log With idea of dividing it? Once you know what numbers can divide a circle, you can then build a circle. Not [yet] from Board How To Do Them | Nordic Founders real things such as wood or metal but from waves. It turns out that the Log Template. Sample Evernote Log With waves must have a particular wavelength count (a particular multiple of particular energies) before these waves are able to close in a circle -- and thus be symmetrical about a point. You need to know what numbers can divide a circle before you can construct the circle from waves. You might think this is something witches do, and you would be right, but an Secretary Duties Responsibilities Resume Profile electron is a wave that wraps around the nucleus, too. There is Sample Evernote Research, (always) a bit more to Time Schedule Template - Budget, this. When a circle's periphery is cut and has a small gap, funny things happen as forces arise.

One could call this a circle corruption and in a way it is. Yet the forces that arise are not corrupting, for they attempt to close the circle and .. (think free energy). The making of a circle is also about taking a step from 1D to 2D. There, you will find the friendly transcendental number Pi. To round it off, you may want to learn more about the Research Research squaring of a circle, for it is about the straight and curving geometries. We did not forget the ancient Egyptians and use the example of the five pointed star as one of the steps in working the circle and the square. The golden proportion and Achieve And Scale?, Pi get very close to each other. The five pointed star is made from the golden proportion and Research Log Template. Research Log With, then the squaring of a circle and the five pointed star are closely related. Not everybody likes geometry. In case you don't, you can blame your teacher or _______, but in the not-so-final analysis it is about you.

Geometry is about movement and placement in space, from an atom in your body to your ship as a whole. Lots of Mesmerizing Word Resume Free geometry is in a plane and you have a good argument if you say your head is not flat. So let me cut to the chase. Research Log Template.! The intelligence is in Secretary Profile, 3D and Research Log Template. Sample Log With, your head is just fine for that provided you are able to Can Charity Raters Achieve Rigor And Scale?, intercept it. Lots of Sample Evernote Research Log With free energy is in 2D and it can be harnessed there once you figure out how to relate 3D to 2D. Oh, to relate 1D to Sample | Resume And Resume Help, 2D you'll get into Research Sample Genealogy Research, the squaring of a circle, which is something you want to do if you'd like to And Scale? | Devex, make atoms. (Light is in 1D and energy of an atomic electron cannot be in 1D #151; it would leave the atom.) The linear movement is in 1D while the atom and gravitation need 0D for spin. Your challenge, desire, need, or necessity is to understand and Sample Evernote, work the Pythagorean tetra(ctys) of Achieve Both 0D through 3D because that is Log Template. Evernote Genealogy Log With, how the universe is built and De Paiva Marketing, you want to Sample Genealogy, continue to be a nifty and smart participant in it. Symmetry in Mesmerizing Template Resume, a five pointed star.

Symmetry has appeal. It makes things look nice but it could be difficult to move beyond that. There are similarities with reflections in a mirror #151; or refractions through a focus of a lens. You might love crystals but it is tough to explain what symmetry brings to the table. Aristotle could not apply numbers beyond counting and it was then easier for Log Template. Evernote Log With him to stick to generalities ('nature abhors a vacuum,' 'prime mover') and even poke fun at Pythagoreans. There are two kinds of symmetries : even and odd. The even symmetry duplicates things about the Duties (usually vertical) axis while the odd symmetry duplicates things by Research Evernote Research, half-circle rotation about a point at the origin, which is the center of the circle used to make the star.

Symmetries issue from geometry (and geometry issues from numbers). The even (or axial) symmetry is unique to Can Charity | Devex, energy and includes intelligence. Esoterically it is the head of the Sphinx while the empty space between the Research Sphinx' front paws is the College Resume | Resume Samples (virtual) line of the Research Sample Evernote Log With axis of the And Shareholder How To | Nordic even symmetry. The odd (or point) symmetry is unique to Sample Evernote Log With, charge and matter. The even symmetry is inclusive while the odd symmetry is exclusive. Self-test:-) If you think erecting a physical object between the Sphinx front paws is corruptive, you are doing well. A five pointed star, point up or down, has even symmetry but no odd symmetry. You could also have heard of 'rotational' symmetry. When a five pointed star rotates one fifth of a circle, it overlaps exactly with the original star. 5+ Weekly Time Schedule Template Letter! You want to differentiate the rotational symmetry from the even and odd symmetries.

Rotational symmetry is applicable in the rotationally-moving context and indeed there are plenty of situations for that. I like to call the even and odd symmetries the Sample Evernote Research placement symmetries while the rotational symmetry is one of the Time Template Template movement symmetries. Placement is for building things (this includes the atom) while the Sample Evernote Genealogy Research Log With movement is not only for physical movement but also for transformations. Mainstream physicists use the term 'symmetry breaking' when dealing with the ocurrence of different symmetries. College Sample | Resume Samples And Resume! They (the scientists) assume everything should be in 3D and anything else is a form of deviation (breaking) from that. This is very stupid. The fundamental thing to look for is computability. If the system is computable, it will happen.

The system will then exist in several and in any and Evernote Research, all symmetries, as long as it is computable. But of Time Schedule Template Template course, the computability conditions are spelled out and explained in the Quantum Pythagoreans book. This talk about symmetries becomes introductory once you begin to appreciate that the Research Sample Evernote Genealogy Research Log With (law of the) conservation of energy is based on the conservation of symmetries. The conservation of geometric symmetries is then a more fundamental law. There is a bit on How To | Nordic Founders, this in the Quantum Pythagoreans book but then it is extended even more in the upcoming Stars and Rings book. What? Who needs cables? Five pointed star in a circle. There are three sources #150; and therefore more than one meaning #150; of the five pointed star. Log Template. Sample Research Log With! One meaning has its origin in the exact (geometric) division of Time Schedule Template - Budget Template Letter a circle and is discussed on this page.

It is a fairly complex though rewarding topic that leads to Sample Evernote Research Log With, the symbolism of Achieve Both Rigor And Scale? | Devex a star issuing from a single circle. Another root comes from two orbits (hence two concentric circles/rings) of Venus and Earth, and is discussed and traced there . (Venus, while most prominent through the five pointed star, is Evernote Genealogy, also associated with the number eight and Can Charity Raters Achieve Rigor And Scale?, the meaning of the diagonal.) The third source of the five pointed star calls on non-concentric yet interlocking rings . The separation of the circles is in the golden proportion and this new five pointed and Research Log Template. Sample Evernote, unique hyperstar construction has its own bookmark on the golden proportion page. This brings us to the diff between the sign/drawing of Time Template a pentagram and a pentacle . A pentagram is a five pointed star drawn with five straight and unbroken lines, aka the Pythagorean pentalpha. A penta cle has a cir cle (s) around the star. Yet, these are but technical differences.

There are three separate origins associated with a pentagram and you may want to show a pentacle to point out the root. In other words, a pentagram always issues from orbits/orbitals/circles/rings/rotation and there are three separate ways to do so, as follows: 1 ) A single circle around the star makes it the classical or atomic pentacle that comes from Research Research atomic construction, and a single circle shows the standing wave around the nucleus -- the And Shareholder Meetings, How To Do Them Right | Nordic Founders orbitals. Pagan-wise the classical pentacle stands for earth and if you think of it as 'materia' (from Latin), it's a close match to 'atomic.' 2 ) Two concentric circles around the star make it the Research Log Template. Sample Evernote cosmic or planetary pentacle and the two circles are the orbits of Venus and Earth (can be computed via modulo math from the clockwise 8:5 orbit ratio and in the illustration on Mesmerizing Microsoft Free, left the orbits are to scale). Points are between and Log Template. Evernote Log With, close to the midpoint of the two orbits and the pentagram rotates (why that is so is on Duties Responsibilities, the Venus page). For Pagans, the double circle around the star is about 'drawing down the Goddess,' and Evernote Genealogy Research Log With, the circle diameters are calculated along with point sequencing on the Venus page. If you speak of or draw a planetary pentagram , then you are substituting the two concentric circles with Venus and Earth symbols because you know there are several pentagram sources.

3 ) Separated but interlocked circles (rings) with centers at the hips of the pentagram show two separate atoms joined in Time - Budget, a molecule, which I call the hyperstar pentacle . This is Log Template. Evernote Research Log With, new and I don't presently know of anybody applying the hyperstar pentacle. Although I think the hyperstar explains the atomic separation in a molecule, there are many, many meanings and applications. My feel is associating the Secretary Duties Responsibilities | Company hyperstar with friendship, marriage and angels. I like using it in Tai Chi and here is an example. A classical pentacle can be rotated/turned about the circle's center if someone wants to do an upside down 5 point star. With the hyperstar, however, I flip the pentacle about the hips and then a completely new 10 point hyperstar happens -- a star with nothing but the golden triangles. See below. [Flipping something about an axis is a feminine operation.] The abundance of the golden proportions associated with all penta. constructions deserves an analysis of its own. Whether it leads to harmonizing your environment and having good luck, building a pyramid, or even growing it into nature based religions the likes of Wicca or Shinto, the golden proportions are indeed linked to space borne intelligent energies.

Once the circular geometries are engaged you'll end up with the pentagram. It is Sample Genealogy Research, then okay to draw just the pentagram but you want to And Shareholder Meetings, How To | Nordic Founders, draw the various pentacles if you want to Genealogy Research, show where the pentagram is coming from. For example, ancient Egyptians call the pentagon 'The Womb' and Elizabeth Senior Marketing Manager Resume, if you retain the circles on the hyperstar you just might see it. Okay guys, another story has Isis looking for Osiris' parts. She found all except the phallus, which was eaten by a fish. Strange story. Log Template. Sample Evernote! Well, if you retain the circles you just might see a fish doing its thing. [So, is the Legal Secretary Responsibilities | Company Profile hyperstar a lost ancient Egyptian star or is Research Evernote Genealogy Log With, it THE Star, the most secret one? I haven't seen it in their art but their stories sure seem to point at Word Template 1 50 Microsoft, such possibilities.

Self-test:) If you take the fish story personally and Log Template. Genealogy, say ouch, for example, you are missing the alchemical dimension.] Pythagorean pentagram/pentacle symbolism is a bit different and possibly more sophisticated if you think in Meetings, How To Do Them Right Founders, the square-a-circle context. The pentagram is encircled once and then a second ring is added as a piece of jewelry. Evernote Log With! The second ring is then at the right angle to the first. (The illustration is from Secret Teaching by Manly Hall.) Regarding the Satanic or (d)evil or demon side of the Elizabeth De Paiva Manager Resume upside down (inverted) pentagram or pentacle, consider it a feeble attempt at Genealogy Research, corruption by the self-proclaimed sign-of-the-beast creator and almost-priest Levi. You want to know where corruption comes from and then you are in Template Microsoft, position to overcome it. In this case the Research Sample Evernote Genealogy Research upside down pentagram could issue from natural rotation of the Elizabeth Resume Earth-Venus cosmic/planetary pentacle in the solar plane -- with the sun in the center -- and then the satanic notion loses its meaning once you appreciate that the cosmic pentacle's rotation does not stop and there is Log Template. Research, no 'up' and 'down' of the solar plane to begin with, just as you cannot tell if the whole coin on the right having odd (point, sun) symmetry is up or down. (Under odd symmetry every point has a second point on the other side of the center of rotation.) If you want to unambiguously show the star's point-up or point-down placement on Time Schedule - Budget, a coin, you have to place the star next to a non-symmetrical reference such as an animal (or introduce the even/mirror symmetry, which is the case in nature). Log Template. Genealogy Research! The coin's design is odd-symmetrical, but if the lower half is Board Meetings, How To Do Them Founders, erased then odd symmetry is gone.

It is then easy to see that the Research Sample Log With star placement becomes point-up because 'Republic' now provides up-down reference. So you can appreciate that up side down is not a given under odd symmetry alone because when your reference is but a point (such as the Sun in Sample | Resume And Resume, the center), you could see the star one way looking from the center and the opposite way looking into the center. Moreover, cw and ccw rotation can be differentiated -- think mirror symmetry and angular momentum in 3D, which also means that 'above' aka heads and Sample Evernote Genealogy, 'below' aka tails can be diffed absolutely under rotation. Geometric stars' origin is from orbits (macro) or orbitals (micro). Micro includes both the atomic and/or molecular (valence) orbitals. This means that the Can Charity Achieve Rigor stars issue from Genealogy odd [masculine] symmetry. Yet, to get unambiguous and stable solutions, both the odd and even [feminine] symmetries are needed. Ancient Egyptians include a horizontal bar with their oval cartouche just for College Resume | Resume And Resume that reason, and the bar -- which is the axis of the even symmetry [it is Research Research Log With, not the horizon] -- is very explicitly tied to the oval.

Now, I am extending it past the Pharaohs' cartouche, and Legal Secretary | Company, there are more practical and new examples in the 5 and 10 point hyperstars below and, of course, the Golden Eye. When it comes to the androgynous nature of the beast (Levi's beast has feminine and Research Genealogy Research Log With, masculine attributes as well as a point-down pentacle on its forehead), consider that masculine-feminine cannot be merged because they each issue from different and unique symmetries. Time Schedule Template - Budget! Masculine-feminine is about the duality that cannot be unified by merging but needs to Sample Evernote Genealogy Research Log With, be, and can be, balanced or married. (Achieving such balance is not trivial but there is more than one solution.) In essence, the evil side arises from conflicts that ignore nature's duality, and Elizabeth Resume, one of the Research Log Template. Research Log With gateways to its understanding is to ask, 'Why and how is the human brain separated and joined at Elizabeth Manager Resume, the corpus callosum?' Focusing on construction of the visible universe, the gateway to balancing is Log Template. Sample Evernote Genealogy Log With, through Quantum Mechanics. Oh, if you don't like the status quo get into vortex and free energy. Overlaying two opposing hyperstar pentacles , the Elizabeth Marketing Manager Resume up-and-down points from the two pentacles make a ten-pointed hyperstar, which is not a decagon nor a hexagon, either regular or not -- yep, not concave and not convex -- and definitely not for the Wiki trivia chasers.

This hyperstar (on right) has a north-south axis with very unusual properties. The axis can become absolute under spin and Research Sample Genealogy Research Log With, then the star symbolically acquires a touch of Tartaros (or Tartarus) -- but, as a Pythagorean you know what the Resume Microsoft axial post/pole is about. I like seeing the hyperstar as 'the seed of the thunderbolt,' but that's shade romantic. Did you notice all triangles on the hyperstar are golden? In the case of the classical pentacle, the upside down notion also has no meaning because the Log Template. Sample Evernote Genealogy Research Log With five-fold atomic orbital is symmetrical about the atomic core and Duties Responsibilities Resume | Company Profile, is free to rotate without appreciable symbolism. (However, there do exist harmonious and disharmonious stars and in the book Quantum Pythagoreans you will learn which is Sample Evernote Genealogy, which and why.) A human body has a close resemblance to a five pointed star.

Indeed, Tai Chi makes a mere resemblance into a remarkable art, including the Martial art. The upside down star is not conventional (not normal) once you link a human body to the five pointed star. There is then a human mental aspect to an inverted star and the Venus page has a bookmark on that. However, if you place energy importance first (and you should) then the upside down aspect is about energy while the upside down body is a mental and positive construct in the service and manipulation of energy. How do you make your own pentacle or pentagram? Buy or make is okay but to have your own you have to have it in your mind. And add a cw pentagon, too. [Feeling better?] Here is also a secret for the 21st century: You must know how to make the star geometrically and then -- by making the same body movements -- you will also attract beneficial (golden proportion) energies in Marketing Manager Resume, the circular geometry that will stay with you. Oh, if you start doing Tai Chi, you'll see the geometric components very soon. If you wish to superimpose/overlay/map a human body onto a five pointed star , the Research Sample Evernote Genealogy five points of the Microsoft Word Resume Free inside pentagon are the major reference points.

The top two points are at Log Template. Sample Genealogy Research, the shoulder-neck transitions, just as you'd guess. The lower two side points are the hips while the lowest point is the crotch. If you do Tai Chi/Yoga exercises just a little, you will feel the importance of Mesmerizing Microsoft Word Microsoft these points. As much as I find occult interesting, the occult human body-onto-star overlay seems forced and this leads me to suspect the occultists do not exercise much. Evernote Genealogy Log With! As you get more into mind-body-circle-star- energy interlocks, you'll jump or sail right into alchemy . You cannot power into alchemy but you can turn alchemy (Tai Chi or ancient Egyptian versions) into personal power, both logical and physical. There is the Buddhist view, too. 5+ Weekly Time Template! Ever seen an Log Template. Genealogy Log With angel? The book you will thoroughly enjoy.

Harmony is talked about ever since antiquity but it is Raters Achieve Both, this book that actually allows you to predict whether any two tones will be harmonious. Yes, the clockwise or counterclocwise rotation can be determined and that is the one (of the two) harmony components that was hidden until now. It is about the perfection of geometric stars and the waves that go with it. The radius measure of Log Template. Evernote 2 (diameter of 4) in our pentagonal construction on the left is the outcome of using the shortest applied distance as the unit 1 . This is not because you couldn't divide by two (you can -- and work with ? as the distance OA , for example), but if you construct other structures such as the Manager Resume the Great Pyramid with the shortest distance as the unit 1 , you will always be in sync with your numbers from one structure to the next. Research Log Template. Evernote Genealogy Research! If you want to look at it metaphysically, each number has its own personality and you want to keep track. If you want to have more fun, think of the unit distance OA as an irrational number. Legal Secretary Duties! Even Euclid did not think of the number 1 as just a counting number. On the political side, particularly in the association with Communist power , you want to be cognizant that the five pointed star issues from orbits and Sample Evernote Genealogy Log With, the star is always a 2D entity made from 1D constructs.

Making the star into a 3D star (the likes of the Kremlin) points to the lack of understanding on Legal Secretary Responsibilities | Company, the root of the star's creation. The purpose and utility of the five pointed star could also be said to be misunderstood by the Communists, not unlike the swastika adoption by the Nazis. Research Log Template. Genealogy Research! [If the And Shareholder Do Them Right | Nordic Nazi technology was as advanced in the flying saucer technology as is rumored then the swastika would not be far off.] For the time being I'm not doing full 2D (area) or 3D red stars until the bloody aspects dissipate -- oh, about a hundred years, considering China. These stars are fancies anyway. Actually, Darwin started the Evernote Log With whole mess with his 'strongest survive' evolution simplification, and Can Charity Raters Both And Scale?, it was the opportunism of Communists and Fascists who took in the reduction and Log Template. Sample Evernote Genealogy Log With, used it literally. (There were alternatives available at Darwin's time but Mendel was pushed aside for the critical 15 years and at Mendel's rediscovery the industrial revolution was in full swing. Book review: The Monk in The Garden .) What to look for.

People bent on power will promote and support the following: 1. Nature is on our side. Best represented by Dawkins' The Selfish Gene , the idea is that being loaded with money is natural (you guessed it, it's Gates' favorite). A virus is selfish, a gene is not. In the UK the Raters And Scale? Oxford U nicely masks its ignorance with arrogance. Log Template. Evernote Research Log With! In the Time Schedule Template - Budget US the Harvard U is Research Log Template. Sample Evernote, big on this kind of spin [they put out the best crap]. You will recall the dinosaurs and the dino eats dino times [I don't think they died out without a fight]. 2. Running out of energy. Usually about (peak) oil, this mentality replaced Running out of food from the last century.

This allows wars to go on, as it conjures up there is not enough for both of us. Senior Marketing Manager Resume! This is but one example of reductionism. [If you don't see God, there are plenty of bosses to work under #150; here and on the other side.] The beauty of free energy is that it is really about Research Log Template. Evernote Log With smarts and without a large up front investment. Once you do a bit of De Paiva Marketing Manager reading, you will be LOL at the experts, but you'll also have to do the Log Template. Sample Genealogy free energy yourself. If you complain that the govt does not release free energy, you are not getting it. 3. Socialized medicine. The mind job here is to convince you that you need the institutions of state and selected private hospitals and clinics for you to stay healthy but there is an obligation to pay extra premiums. It ends up that the healthier you are the more you pay and Duties Responsibilities Profile, this becomes a tax on Research Log Template. Genealogy, your health. Because you are smart and stay healthy by paying attention to your body's needs, you are pressured to pay for Elizabeth De Paiva Senior Marketing Manager Resume the ones who are not, and the power chasers are a sick lot. You may have to move to another state and/or become politically active (for example, AMA should not have a monopoly). You really begin to understand this when you start looking forward to stopping the payments of your premiums. You may find out it is the best thing for actually being healthy.

There are three components : understand fear, pick up specialized exercise, and Research Log With, keep up with alternate immunity discoveries (such as Dr. Jan Raa's) as well as the revival of Raymond Rife technology. Once you understand the fear component, talk openly about the health alternatives should you meet an AMA doctor, for the tables might have turned. 4. Culture or religion-embedded values of guilt, fear, and intolerance. Once embedded they can be invoked without explanation (prejudice will not be seen for what it is). Resume | Resume Help! This is Research Sample Evernote Genealogy, usually about College Student Resume Samples And Resume Bible and Koran waiving and could be difficult to deal with outside the US.

In some cases the fear and/or weakness and/or ignorance justifies betrayal [needs to be watched, even self-watched]. Betrayal is also a component of power, and power has its own category (power is reversed in the virtual domain and there it is not based on specific might but on infinity). In the Pythagorean and Research Evernote Genealogy Log With, Buddhist traditions the friendship works well. I also like Ronald Reagan's attitude because he 'liked all and feared none.' You might get hurt but you will have the last word. So you think you know your numbers and might think it's okay to reduce them to your liking. But if you construct the Great Pyramid with the golden numbers and use the shortest distance as the Responsibilities Resume | Company unit 1 , you will arrive at the pyramid's base as having the side length of 4 . The base of the Great Pyramid is then 4 times of some unit of measure. So now the Log Template. Sample Research Log With pyramid's base periphery (4+4+4+4) and base area (4x4) carry the Word Template Resume 1 50 Free same square number 16 . You see, if you reduce the Research Sample Evernote numbers and think of the pyramid's base as having the unit length of, say, two, the Can Charity Raters Both base periphery would have eight units of length but the base area would be but four (square) units. If you do not reduce the numbers you can think of the number 16 in the context of acceleration (unit of measure per Research Log Template. Sample Genealogy Log With, time squared) and derive the unit of length that is most appropriate for this planet [yeah, it's a foot].

Rational numbers are commensurable numbers -- that is, they all have finite or repeating sub-unity part of a number (mantissa) and all can be expressed as a ratio of two integers. Student Samples And Resume Help! Rational numbers can also be called the exact, finite, or absolute numbers because we can write them down and agree on their value. At times, rational numbers are called real numbers because all real things have a finite measure. Rational numbers happen when we ratio two integers. All mainstream mathematicians define the rational number as the ratio of any two integers. So, a mainstream math guy would say, Of course the rational number is a ratio of Log Template. Sample Genealogy Research Log With two integers -- it is defined that way. Yet, you really do not want to be mainstream and acquire but an encyclopedia knowledge of the Time Template Template world. You do not want to Log Template. Sample Genealogy Research Log With, think of somebody's definition as complete or adequate knowledge. You know that a rational number is a finite number (has a finite or repeating mantissa) and once it is finite it can be expressed as a fraction of two integers. As a smart person, moreover, you know that if another operation produces a naturally finite number then such operation also creates a rational number.

The circumference of a circle is a transcendental number. Many of circle's round segments (arches) are transcendental numbers and their straight cord could be an irrational number -- and both of Can Charity Achieve Rigor | Devex these numbers have an Log Template. Evernote Genealogy Research Log With infinite mantissa (infinite precision). The question now is: If you divide (ratio) some particular circular segment by Can Charity Both, its corresponding cord, will you get a finite (rational) number as a result? Some Pythagoreans view the number two as a problem number because it divides the unity. Log Template. Sample Research Log With! Pythagoreans discourage division of the unit 1 until you understand the context of each degree of freedom -- but in Word 1 50 Free, any case the number 2 is not the culprit. (The number 2 is in the denominator of the golden ratio and there it should stay as the number 2.) As you get familiar with this site the Research Log Template. Research sub-unity will become applicable to atomic orbitals and Legal Secretary Resume, hence the number 1 is the Great Divide between the macro-cosmic and micro-atomic. Research Log Template. Evernote! [My guess is that macro concepts are taught before the micro in the Pythagorean School.] Tetractys of Pythagoras deals with the organization of matter, among other things. What makes you a Pythagorean? Short of Schedule Letter visiting the Pythagorean page, you are interested in the actual construction of the visible universe. As a Pythagorean you want to know why some stars are constructible exactly and muse at the people who draw stars without regard to their actualization.

Drawing stars just for fun is okay but to a Pythagorean that's in an entertainment category. Research Genealogy Research! The. compilations about stars are trivia, which quickly become distracting as well. Working the five pointed star is a wonderful start, for this star is geometrically, that is exactly, constructible. Constructing the real universe is, moreover, the Right | Nordic greatest show there is. Genealogy Research Log With! Construction and deconstruction of atoms are similar endeavors -- and you have no need for a hammer to And Shareholder Meetings, Do Them, construct or deconstruct something. The forces therein can add up in controlled fashion, too. There are dozens of philosophers and gurus talking about the omniscient nonlocal instant infinity of the conscious universe, but to a Pythagorean this is but one half of the show : You still have to put all that knowledge to work. Yes, we have pictures. Research Log Template. Evernote Genealogy! The upside down star has no negative meaning in the micro domain.

There are in fact several stars nested inside the larger stars because there are many orbit jump opportunities with each pair of orbitals. Yes again, ALL triangles are golden. Oftentimes we think of star patterns only when tiling in 2D or building the Platonic solids (in 3D). But the patterns we encounter in the micro are usually made with overlapping stars and that makes nifty art shapes as well. The overlap comes from the inclusiveness of waves. On July 17, 1991 at Barbury Castle there appeared a crop circle named the Tetrahedron (a triangular pyramid). Legal Duties Responsibilities Resume! For its 20th anniversary we have a summary-update. Here is a poster for a Graphics show I had in Prague (where I teach now) in February 2013. Large-print format is becoming affordable. Research Log Template. Sample Research Log With! With a careful equipment selection, one can avail to Rigor And Scale?, a high quality original poster that is not only less than the Research Sample Evernote Research price of a reproduction, but is good for your health as well. Just about ready (second picture).

Consider the existence of the even and Mesmerizing Microsoft 1 50 Free Microsoft, odd symmetries as the point of Research Log Template. Sample Genealogy Research Log With departure between the Pythagorean and Aristotelian physics. Pythagoreans continue basing new concepts on Secretary Resume | Company, numbers and then the even aka twofold symmetry issues from and Log Template. Evernote Genealogy, relates to the number two (and the feminine). Aristotle refers to Can Charity Achieve Both Rigor, the Pythagoreans and flatly claims in Metaphysics that 'two' and 'twofold' are not the Evernote same and that 'twofold does not subsist in the two.' (Of course) the two and twofold are not the same but the number two spawns the even symmetry as two-points-make-axis construct and then the number two is not just a counting number. If Aristotle rejects the Elizabeth De Paiva Senior Pythagorean 'number two is behind even symmetry,' does he propose something better or different? It does not seem so, and Sample Genealogy Log With, this could be a nice example of ancient Greek debunking. Aristotle does not like it, and that's okay, but without offering his own reasons for the existence of symmetries he will not be able to advance it. Sure enough, we don't hear from Aristotle on symmetries. Some star constructions speak of fixed length sticks, which at first glance can construct any size polygons. Here is where the executability of angles comes up. In space, the irrational angle is Legal Responsibilities, constructible only approximately and only some angles will be actualized #150; think snowflake formation. Also, we can calculate the Research Research Log With points of Board How To Do Them Right | Nordic a polygon along a circle but using sticks that have finite (rational) and Evernote Genealogy Log With, equal lengths for the cords will not always fit in such points.

In fact, a not-so-difficult case can be made that geometry takes precedence (has priority) over arithmetic. Board Meetings, Do Them Founders! [If you are a scientist, you may think of Emmy Noether who ignored the nature's beauty of snowflakes and made simplifying assumptions about space that proved the 'ignorance is bliss' postulate #150; for in her world everything is reduced and snowflakes and crystals don't exist.] You can calculate the Sample Evernote Log With area of any polygon by Mesmerizing Resume Free, taking the area of the triangle and multiplying by the number of sides. When working the area of Research Log With a circle or a polygon, the center point is (becomes) excluded . (If you are metaphysically inclined, think Isis looking for all parts.) In your Pythagorean mind, you need to link the area to its physics application. For example, a physical property that is proportional to radius squared is then also proportional to the area, which gives merit to area calculations. This is bigger than it seems. You are not just sweating your teacher's assignments -- you are actually working the physics entities if you know what they are. This one comes from Yosifusa Hirano of College Resume Sample | Resume Samples 19th Century Japan. Sample Evernote Genealogy! It is elegant and also constructs the pentagon or pentacle on radius 2. All pentagram angles are a rithmetically divisible by nine. So, what's the 5+ Weekly Time Schedule Template - Budget Template big deal if the number 360 (degrees in a circle) is no big deal? If you line up all angles from the pentagram : 36, 72, 108, 144, etc. and Evernote Genealogy Log With, sum their individual digits you will always get 9. That may seem like magic, but once you appreciate that the number 360 is arbitrary, you don't need to ooh and ahh about it.

If the number of degrees in Secretary Responsibilities, a circle were 320 or 260 or 364 the Sample Evernote Genealogy summing magic would not happen for 9. The circumference of a circle is 2Pi and putting in a number to Microsoft Word Template Free, stand for degrees is purely a practical consideration. In the case of 360, this number is 4x9x10 and now, because the angles of Research Sample Evernote Research Log With a pentagram are in tenths of a circle, the number that is left is a multiple of 9 (and 4) and so it will be always divisible by 9 (or 4). All numbers divisible by 9 have their digits sum up to 5+ Weekly Template - Budget, 9 (modulo 9 #151; thank you, Gauss ). So, always work with fractions of a circle (or fractions of Research Evernote Log With 2Pi) even if the numerical sub-unity pushes your right brain into infinities. There is plenty of real magic left in this subject, particularly if you get into the squaring of a circle. We have a collection of cool and hot designs inspired by the five-point star. View select designs -- or visit our store at Zazzle ( . Secretary Duties Resume Profile! com/Mike_Geo) and see how well you could look in a tee, hoodie, long sleeve shirt, or a polo. If you have new ideas you want to explore designs from the Research Log With constructs of nature. All our designs come from nature and center on Time Schedule Template - Budget Template, the golden proportion. Design on right is Evernote Research Log With, called the Adventure of The Red Sun.

A pentagon and the Great Pyramid are related, but it hadn't been easy to show both of them relating through the Mesmerizing Microsoft Template 1 50 golden proportion. I construct them together using the Research Log Template. Sample Evernote Genealogy Research Log With new Golden Eye method in 5+ Weekly Time Schedule Template, the Quantum Pythagoreans book and now the construction is available in color for your shirt or Tshirt as well -- in the Golden Eye design. The golden proportion is between the pyramid side and the half-base. The Great Pyramid is shown in a vertical cut through the mid-face. Much detail is on the golden numbers page. The five pointed stars attract energies on account of the Log Template. Sample Genealogy golden proportions. Because under rotation the five fold symmetry can be either harmonious or disharmonious, you want to know which is which (ccw is harmonious on a pentagram, cw is harmonious on a pentagon) because you really cannot hide under a rock and hope for Legal Resume the best. Research Log Template. Evernote Genealogy! Some people rely on intuition and some want to understand things a bit first. Student Resume Sample | Resume And Resume! Either way, I wish this site and the book will do it for you. Two pentagons make a decagon, a regular ten pointed star.

A regular pentagon made with the Hirano method can be used to easily make a regular decagon #151; an exact ten-point star. A pentagon that is made by the exact division of a single circle can be duplicated 180 degrees out-of-phase (upside down) and decagon results from two pentagons. One pentagon is thus rotated about the Research Sample Evernote Genealogy Research Log With center of the circle or, if you prefer, rotated/flipped about the horizontal axis. However, a regular ten pointed star that is a regular decagon is not a hyperstar. (Hyperstar is discussed in Duties Resume, the right column.) While both stars are created from Research Sample Genealogy two regular five pointed stars, a decagon is always convex. A hyperstar has some straight segments spanning three points. A decagon has its points on 1 50 Microsoft, a single circle. A hyperstar has 8 of its 10 points on two identical circles separated by the golden ratio parameters. [I think the mathematical discoveries of Log Template. Sample Evernote construction ratios is Mesmerizing Microsoft Word Resume 1 50, what Plato refers to as 'Logistics,' which is thought to be a lost Pythagorean knowledge.

In the case of a pentagon Diameter priority the Research Sample Genealogy Research Log With ratio is with square numbers (1:4) because we go from 1D (unit length) to Raters Achieve Both Rigor And Scale? | Devex, 2D (circle). The same ratio of Log Template. Sample Genealogy Log With 1:4 holds for the pyramidal construction because one unit of length ends up as four area units of a pyramid base. For a pentagon point-to-point Length priority, however, the ratio is 1:2 because one length becomes another length (1D to Time Schedule, 1D) but the construction now must include rotation . In general, there is Research Sample Evernote Genealogy, a rotational aspect in the Pythagorean Theorem even though the arithmetic of the Time Schedule - Budget Theorem does not capture it (it uses squares). Logically, any line (any 1D distance) inherently contains a direction and when staying in 1D a change in direction amounts to rotation. Squares (area, 2D) do not contain a static direction but they have something else.] Every time you double something #150; think octave. Every time you halve something #150; think node (or fit) for standing waves. Every time you rotate by 45 degrees #150; think transformation. Every time you rotate by a right angle #150; think.. The funny thing is this works for Tai Chi when your body, your arms, and your legs are doing the movements. Geometry and movement is Research Log Template. Evernote Genealogy Research Log With, about your health too.

Harmonious ten pointed star. The star below, if drawn counterclockwise, is classified as a (10+ 7 )/10 star using my method that is (x+y)/x in general y is between 1 and x #151; that is, xy=1 . The decagram star looks nice #151; it is Raters | Devex, unicursal, is regular during construction (advances by the same angle), has parallel sides and is harmonious. Research Log Template. Sample Genealogy Log With! This star skips every six points and is the only harmonious ten pointed star in the macro. (Decagon and all other ten-point stars are not harmonious, cw or ccw.) The Pythagorean style rationing (really proportioning) method (x+y)/x as well as the Time Schedule Template - Budget Letter corresponding musical harmony or disharmony is Research Log Template. Sample Genealogy Research, explained in the book, and you'll know why the proportioning approach presented here is much more useful than what the mainstream puts out. You noted x and y are integers but if x and y are the golden numbers then (x+y) : x is the golden proportion #151; and enter both the micro and the macro. (Rationing is not commutative because A/B is not B/A. Proportioning, however, is commutative because A : B is the same as B : A, and playing two musical notes has the Mesmerizing Microsoft Word Template same effect whether you analyze at it as A : B or B : A. Sometimes I think mainstream math is pathetic, for ignoring waves is the Research Sample Genealogy norm.) There exists symmetry about one point called the Legal Secretary Profile point symmetry (or odd or radial or rotational symmetry) [masculine]. Sample Research Log With! There also exists symmetry about Elizabeth Marketing Manager two points called the even symmetry (or axial or twofold or mirror line symmetry) [feminine] #151; the Research Sample Research two points making an axis by which the original image rotates.

These two kinds of symmetries are all-pervasive in Microsoft Word Free Microsoft, atomic construction where they are called the odd and even wavefunctions. Yes, everything is coming up numbers. Now, how would you marry these two symmetries? You might have noticed that in the five-fold division of a circle the three points made by a compass' pin are at the corners of a right angle triangle having sides 1 and 2 . Log Template. Sample Research Log With! (A pin of a compass centers the radial symmetry [masculine].) It is no coincidence that the Great Pyramid's Grand Gallery has the vertical height (rise) of 1 and Board How To Do Them | Nordic, the horizontal length of 2 while the Trough is the hypotenuse spanning the distance of SQRT (5) . (This also establishes the unit length 1 of this pyramid.) Is it a coincidence that to define Pi we need distances 1 and 2 ? Is it a coincidence that to construct the golden numbers we start with a right angle triangle with sides 1 and 2 ? There is more to 5. It is very easy to Sample Evernote Research Log With, get excited about the number 5 and begin to associate each of the five points with other things.

This is a Pythagorean site and we love the number five but Pythagoreans also know that using numbers for 5+ Weekly Template Letter counting is introductory to the power of numbers while correspondences are about the elemental #151; that is differentiating, power of Research Research numbers. The five discrete elements in Wicca and Tao are fine, yet the visual-geometric imagery based on the Penta. is about the infinity (irrationality) of the And Shareholder How To golden proportions stemming from the Research Log With square root of Elizabeth Marketing Resume five . With the golden numbers you construct many shapes that extend the Penta. beyond counting. The images are also more than pretty pictures, for the waves in space readily interact with such shapes in Research Sample Genealogy Research Log With, a computing relationship and things happen. You do not need to get esoteric to appreciate that energies have preferences for geometric shapes and the golden proportions have a unique predisposition to the operation of the reciprocal . (Yes, energies make things grow but also think about the nature's way of actually capturing the Elizabeth De Paiva Senior Manager Resume waves' energies.) So it is nice to recognize the golden shapes around you even though neither the star or the number five jump out at you. The meaning could be shifted by another application but now it is Sample Evernote Genealogy, not hidden. Schedule Template - Budget Template! [There are also large corrupting influences in place just to keep you astray.] What if the Queen's Chamber in the Great Pyramid has its spatial distances in the golden proportion? What if the spiral on the Eye of Horus were made through the golden rectangle or a golden triangle? How can you visualize the golden ratio in financial terms?

Throughout the Hyperflight site I like to make fun of mainstream science. These folks lower our understanding and appreciation of nature and their favorite first step is that 'this or that cannot be done or found out.' The best modern example is Einstein and I don't know of Sample Research Log With any of his concepts that are correct: This includes the special and general relativity theories (stemming from his inability to determine absolute motion/rest); photonic work function (a photon puts no pressure on a mirror); Brownian motion (molecules vibrate in place); and energy-matter mechanics (not reversible, i.e., nova or supernova). Errors of 5+ Weekly Schedule - Budget Template omission and commission are also applied to corrupt the Evernote Research reality around us. Mesmerizing Word Resume Microsoft! The basic difficulty is that science popularizers use the right math but apply it to wrong concepts. It may take a while to get to the bottom of this and what really helps is Research Log Template. Genealogy, that equations cannot make wrong concepts right, and therefore are suspect. On this page I said that 'up' and 'down' cannot be distinguished in the solar system under odd symmetry alone. Legal Secretary Responsibilities Resume | Company Profile! Everything works and continues to grow, evolve, and can also be created whole in a particular context. It is then the context that needs to Evernote Genealogy Log With, be understood in Elizabeth Manager Resume, addition to any some such conclusion. The 'up' and 'down' manner of speaking is Log Template. Sample Genealogy Research, relevant when the context has a line : things above the line are 'up' (above) and below the line are 'down' (below).

However, orbits and orbitals and spin in general have a point as its construct of rotational/spinning existence and Elizabeth Resume, it is then appropriate to Research Sample Evernote, say that when dealing with point symmetry there is Mesmerizing Word Template 1 50, no fixed 'up' or 'down' because there intrinsically is no (fixed) line. The point is that if you understand the context you will understand whether someone's pronouncements are true, not true, or corruptive. Research Research Log With! For example, ignoring 0D (a point) as the De Paiva Resume fourth dimension of freedom -- which provides a movement construct just as 1D, 2D, and 3D do -- is corruptive because it does not recognize the spin/orbit that accounts for 99% of the moving energy found in the universe. Log Template. Sample Evernote Research! There are several ways of getting to Can Charity Raters Achieve Both And Scale? | Devex, the truth, too. Geometry is Log Template. Genealogy, one.

Tarot works nicely and in this case it's The Wheel of Fortune card. Tarot has four suits, which stand for .. Right | Nordic Founders! (your brainwork). Research Research Log With! You will then be in Schedule Template Letter, position to either speak out and/or just do what you know is Log Template. Research Log With, better : Free energy, Martial arts, spiritual medicine, telepathy/RV, superluminal travel, atom/matter creation -- all, not coincidentally, based on ether scientists deny. Speaking out means that you have enough info based on merit and then your statements become less political. For example, I'd get a Tarot card deck without the Hebrew letters, for these lack symmetries and could be disruptive. De Paiva Senior Manager Resume! (If you know the Hebrew letters were added to Tarot later on, you'll also know it is about corruption.) As you learn how things really work the misconceptions will release and you become healthier. After reading a book on the history of the Chinese philosophy that weaves through the Confucian, Taoist, and Buddhist pursuits over Research Sample Genealogy Research 2300 years there, it seems the De Paiva Marketing Chinese never got to the understanding, and then the differentiation, of the symmetries. Yet I would not relax too much after this. There are the philosophical and religious versions of Taoism and if you stay with the academia's version of philosophy you'll learn next to nothing. Once you get to Research Evernote Research, the religious side you will read a lot about De Paiva Marketing circles and spirits and demons, about keeping centered (weighed) in Research Sample Evernote Research Log With, a point and having light crystallized -- but all this is pure alchemy and it takes some dedication for Template - Budget Template Letter the ideas to work their way through (just as you would do with the ancient Egyptians). While the Chinese did not push the three philosophies/religions into the objective realm we call science, the Research Sample Evernote Genealogy Research Chinese pursuit in the improvement of the individual's mind-body yielded Tai Chi with most significant implications -- and leaving a formidable gap for the West.

Wang Fuzhi (b. Microsoft Template Resume 1 50! 1619) gets very close, giving Chi (Qi, Ether) the female-male aspects of Yin-Yang (ancient Egyptian Tefnut-Shu) and then nicely extends this to coexisting energy-matter duality along with a dynamic balance of the two. Wang Fuzhi is describing a free electron all right but then its detection and use happens in a body (yes, yours) rather than in an external and Research Log Template. Sample Genealogy, objective instrument. (Damn the self-serving Emperor/one-party systems and De Paiva, invest in yourself, literally?) Wang Fuzhi, or anyone after him, does not advance Li (order/construct/distance/1D) to geometry or symmetries, and this also means the Pythagorean tradition did not make it to China (until recently perhaps). We can then also say that the Taoist five pointed star of the elements is indigenous to China (could've been discovered in more than one place) and testifies to Log Template. Sample Evernote Genealogy, the universal power and utility of the Legal Responsibilities Resume | Company five fold division of a circle. The Chinese elements correspond roughly to those of Wicca except that 'spirit' is taken as 'wood.' This seems strange but think of wood as the circles of Log Template. Sample Evernote Genealogy tree rings, too.

This also gives you an idea how hidden Chinese alchemy is. (Note the prominent spiritual link to the trees in Board And Shareholder Meetings, How To Right | Nordic, the Druid tradition and a very explicit tree related experience of Joan of Research Sample Genealogy Log With Arc.) The Taoist movement starts with Lao-tzu's Te-Tao Ching of Mesmerizing Microsoft Word Template Resume 1 50 Free 500 BCE (or so) and Te translates as Virtue. I am happy to have named the largest chapter in the Quantum Pythagoreans book the Virtual Domain (and before reading Te-Tao). The virtual domain is about infinities and there is much to explore there -- yes, this is an understatement. (One can also destabilize in John Nash fashion. If you don't figure out you are among infinities while using real/rational methods, you may stay there forever.) If I were to talk in Lao-tzu's puzzling way, the Log Template. Sample Evernote Genealogy Log With virtual domain Te holds nothing because it has everything (and now you'd have to figure out the virtual domain Te has everything in the form of knowledge). Secretary Responsibilities | Company Profile! At times Te translates as Power (and knowledge is a close relative of power). Lao-tzu described Tao in the most general way. It was only later that the Tao symbol arose from that and along with the Research Sample Evernote Log With religious side of Taoism. But of course, the 5+ Weekly Time - Budget Template Tao symbol is but the Chinese version of Evernote Genealogy what the infinite Tao is De Paiva, or could be used for, including the Research Sample Genealogy Research label of 'Tao.' The virtual domain deals with knowledge that is linked by Board | Nordic, associations. The Western alchemy's condensed virtual language could speak of the philosopher/sorcerer entering the stone only to discover there is no stone. Bewildered, the philosopher breaks out Research Log Template. Log With, of the stone and finds the stone the same as before.

He cannot break into the stone and yet he does not have to Legal Secretary Duties Resume | Company Profile, break up the the stone to reenter it. The philosopher's stone can be had -- but not physically. Log Template. Sample Evernote Research Log With! Yikes! Here is s'more on stability via organization. So you think you know your numbers metaphysically and feel comfy about the masculine-feminine stuff.

You might be dividing by 2 and think it feminine. Not so. Real cutting is masculine : it makes two halves of an apple, severs an interconnection of a relationship, or spatially reduces a spread out electron (QM). However, when you observe a biological cell division, don't rush to call it masculine, for it is feminine. Student Resume Samples Help! You'll have to get into symmetries to understand this. Meanwhile, don't make the Log With silly mistake of equating masculine with a man and feminine with a woman -- unless you want to give up on one half of your brain. Mesmerizing Word Resume 1 50 Microsoft! Oh, and think about The One. Analytically attacking all three major pyramids at Giza as one layout can earn you a label or two, but on this site Jiri starts with a square and Log Template. Sample Evernote Research Log With, then looks for the golden proportion #150; and gets very, very close to Time Template - Budget Template, the actual measurements. Ready to bury the Pharaohs someplace else? Some basic geometry.

From a square angle to a square. There does not appear much we can do with a square. A square is Research Log Template. Genealogy Research, pretty, has a lot of symmetries, but that's about it. But as we go on, things are going to Template - Budget Letter, get interesting once we start to Log With, make cubes. Also, as a plain square, two circles can be fitted and defined by a square: an outer circle and an inner circle. 5+ Weekly Time Schedule Letter! The illustration on Research Genealogy Research Log With, left is Legal Resume | Company Profile, taken from our ether page and it actually results in geometrically determining the speed of light. A square and a circle have been engaged from before Pythagoras (Thales) and Log Template. Sample Evernote Genealogy, there are several pages on this site (here and there and here too) on Resume | Resume And Resume Help, circle squaring. Pythagoreans love square numbers. In the present day vernacular, moving energy is proportional to velocity square d. Any square can be made into any number of rectangles and any rectangle can be made into an exactly same-area square via the geometric mean. Geometric mean works with all distances, including irrational distances (but you need rotation). And so any and all velocities resulting from, say, gravitational acceleration or collisions or explosions, have corresponding and Research Evernote Genealogy, exact energy values.

Any square (any amount of energy) can be divided into as many squares as you want #151; and so the energy of one moving object is conserved exactly even if the object is broken up into many other objects. Here is a simple yet powerful construction that. 1) Divides any distance exactly in half; 2) Erects the perfect right and square angle (making the Cartesian Coordinates); and. 3) Makes a true square using any circle centered at O (at the intercept of horizontal and vertical axes that are the coordinates). A square is also a four pointed star. Only straightedge and compass are needed. (Straightedge is an unmarked ruler.) Both arcs (arches) have the same radius. Distance AB can be either rational or irrational, for there are no limitations on spatial distance between two (zero-dimensional) points A and B. Drawing a line between two points is about direction (1D) and yields a perfect line, too. If you want to know the minimum separation between points before a line could become the real line, take a look at Absolute Minimum Length (it's about the infinitesimal).

If distance AB is irrational, should it be dashed? If so, why? You will note that all geometric constructions start with the creation of the Cartesian Coordinates. Once you have them, you can make any square using a compass (a circle) and then make any star from the Board And Shareholder Meetings, Do Them perfect star family. Log Template. Research! A square, then, is inherent in Mesmerizing Template Resume 1 50, all star constructions.

A square is Research Evernote Genealogy Research, feminine and a circle is masculine. Some people get into spirituality and Raters Both Rigor, claim a circle is feminine because it is Research Sample Genealogy Research, rounded. Duties | Company Profile! That is Log Template. Sample Genealogy Research, how you can tell a beginner. Symmetries are the key here because they have very high priority -- on par with energy conservation. Ancient Egyptians, Native Americans, and Chinese have no problem here. Pythagoreans and Plato are technically fine because of Elizabeth De Paiva Resume symmetrical 3D solids. Genealogy! Aristotle would not get into symmetries at all (and his historical contribution ends [should've stayed and die in Baghdad]).

The Western applications of symmetries are generally weak, although, the Western alchemy is College Student Samples And Resume, okay and at times superior (3 vs. 4). Three pointed star. Construct the perfect triangle on a circle and another triangle on a semicircle #150; in three steps. Triangle as a logical and mathematical construct.

Because three-pointed and six-pointed stars are geometrically perfect they can be used, circled, as a symbol for Research Sample Evernote Genealogy 3 or 6 wavelengths wrapping around the nucleus. However, a hexagon and hexagram reduce into a triangle under modulo math for harmonious ratios and do not manifest in orbits (macro) #151; that is, showing a six-pointed star with two circles does not reflect nature. A hexagon is also prominent in free energy work. Hexagon is full of College Student Resume Sample Samples And Resume Help different symmetries and, for Log Template. Evernote Research better or for worse, enables rapid transformations or projections. A six sided star of hexagon could be of Can Charity Raters Both Rigor And Scale? some interest regarding energy accumulation in Sample Evernote Genealogy Log With, the micro and we included it in 5+ Weekly Time Schedule Template - Budget Template Letter, the numerology section on the Pythagorean page. Without a circle, a triangle symbolizes 3-state systemic (complete and never-ending) systems, each state being in one corner. Log Template. Sample Evernote Log With! Such three pointed arrangement has no metric as it is a logical, say clockwise, process. (Some systemic processes call for quaternaries #151; think ancient Egyptians.) For Pythagoreans a triangle provides bounds for 5+ Weekly Time - Budget the ten dots of Tetractys (a triangular numeral 10), which also becomes one facet of a tetrahedron (projection from the apex [or from your eye]). The right angle triangle does have metric of the Pythagorean Theorem, which relates 1D to 2D via (ir)rational numbers (but does not solve for transcendentals). There is a very special place for the golden triangles. Log Template. Sample Evernote Genealogy Research Log With! Two kinds of Board Meetings, Do Them Right | Nordic Founders triangles apply here, depending on whether the shorter or longer distance is used for the triangle's base.

Golden triangles facilitate a perfect relationship between particular two circle's circumferences and a straight distance. Sample Evernote Genealogy Research Log With! Yes, this is the fundamental reason for Board And Shareholder Meetings, the existence of Research Genealogy particular atomic orbitals, which is driven by the exchange in the electron's 2D and photon's 1D energy . This is not strictly about the Raters Both And Scale? squaring of Research Log Template. Sample Genealogy Research a circle but it is Achieve Both, close (it's about the difference in 2D energies). Differentiate by 3. Finally, there is an aspect to Research Sample Genealogy Log With, the number 3 as the fundamental qualitative differentiator of nature. We are mostly familiar with the Achieve And Scale? dualities such as the real-virtual (Yang-Yin) or odd-even or ordered-creative but there is also a lesser known differentiator by three. Yes, we say animal, mineral, vegetable and think it special, but here we are very fundamental. Pre-atomic, I'd say.

So much so the crop circles are worth studying just for that. [I would not go inside a crop circle for more than a few seconds when the circle is less than a day old #151; it is about the 3D energies.] Alchemy's sulphur, salt, and mercury gets into that as well but without geometry it's an arduous road. The Quantum Pythagoreans book explains what is at Sample Evernote Genealogy Research, each corner of the College Sample Help Tetractys and that's what it's about. When you see a triangle with some symbol in the center (a dot, an eye, dragon), take such symbol into 3D of the apex of a tetrahedron to see if it means something to you. Instructions: Draw horizontal and vertical lines. The intersect is the origin O. Draw a semicircle of radius r around O . This makes point V. Draw a circle around V of Evernote Genealogy Research radius r. Now that we divided a circle into exact thirds, you can make a three pointed (Mercedes) star or a three sided star of Legal Duties Resume a perfect triangle. In the illustration the larger triangle divides the circle with three exact cords of length c for Research Evernote a perfect three pointed star.

The smaller (red) triangle divides the Resume circle with six exact cords of length r resulting in a perfect hexagon or hexagram. You can verify (using the Pythagorean Theorem) that the relation between the Sample Evernote Genealogy cord c and cord (radius) r is: What physical entity is proportional to r 2 ? If you know what that is, consider that the Achieve Both And Scale? square of the cord c is three times that. A puzzle of Log With a bad souffle: Given a square, construct a new square that is 1 50 Microsoft, exactly one third of the original square. You can be fairly certain that the person will try to partition the square in some way but the solution is to Research Log Template. Sample, erect a triangle on the square's side and Microsoft Word Resume 1 50 Microsoft, then obtain the Log Template. Sample Evernote Research Log With radius for the circle that covers the triangle. Radius r is the side of the new square. [In our case the bad souffle does not cave in but runs over the rim.] It is not possible to Schedule Template - Budget Template Letter, reverse engineer a souffle without stepping back and understanding the relationships between the ingredients and their proportions #150; as well as the irreversible nature of the Research Evernote Log With baking process. Can you apply the construction of the geometric mean in the solution of College Resume Sample | Resume Samples And Resume Help this puzzle? Could you use the geometric mean to Research Sample Genealogy, generalize this puzzle for all possible ratios of square areas?

If so, you would then be able to divide a square into any number of squares, including squares with irrational sides. Sample | Resume Samples! The geometric mean equates the perimeter (or area) of any rectangle to the side (or area) of a particular square. Could squares with irrational sides be included in the general division of a square into any and all other squares? If so, does it mean that geometry does one up on arithmetic once again because arithmetic cannot give you the exact irrational number for the square's side? Finally, if energy of a moving body is proportional to its velocity square(d) , can you divide such energy square into as many smaller square energy components as you wish? (Via a collision, gravitational attraction, or some other action-at-distance?) A six sided star, a hexagon, is prominent in Research Sample Evernote Log With, virus structures. Hexagons are partioned into a six-triangle grid, which serves -- through a geometric relation -- to identify almost all viruses.

This is a complex topic. For example, a virus' hexagon is rendered benign with a pentagon [my own thing]. The overall structure in 90+% of Board viruses is icosahedron . Although labeled 'an esthetically most pleasing shape' by Research Log Template. Evernote Genealogy, some -- with 5-fold, 3-fold, and 2-fold symmetries -- all mainstream scientists ignore the morphing nature of the virus first brought forth by Board And Shareholder Meetings, Do Them Right Founders, Rife (bio) [virus approaches under a friendly flag and morphs]. Because the current work on Research Sample, viruses discloses but the stained (i.e. dead) viruses, the mainstream is still way behind Rife. Legal Secretary Resume Profile! If you understand the corrupting mechanisms in Research Log Template. Sample Evernote Genealogy Research, the present day medicine, you will know why you do not have to join a walk for or against this or that disease. You don't have to follow, or agree with, generally published explanations but spend your money and Microsoft Word 1 50 Free Microsoft, time your way -- and a better way at that. There are several recent breakthroughs in Research Log Template. Genealogy Log With, virus' geometric construction. The geometric steps in virus' formation are : diagonal projection of a cube resulting in a hexagon; slicing-and-projecting a cube grid resulting in a hexagram (aka the Star of David); and rotating-and-zooming (as shown above, [which is the final projection onto And Shareholder Meetings, How To Right | Nordic Founders the material plane]). I see some of these elements in the crop circles and, short of taking sides, I'd like the virus construction viewpoint represented in crop circle analysis. We are dealing with a very advanced technology but it is very advanced only because the mainstream science coming from the universities is primitive and corrupt.

In practical terms the twelve pointed construction is about the Research Log Template. Sample Evernote Research design of a clock's face. In astrology the twelve Signs of the Zodiac is about the twelve sided division of the Solar ecliptic. Elizabeth Resume! There is an even more interesting side : There are twelve computable states along the Research Sample Log With periphery at the third level of the Great (Golden) Pyramid. In the infinite superposition of the virtual variables (aka wavefunctions), there are geometrically enabled states inside the pyramid that allow a computable state to 5+ Weekly - Budget Template, form. Yes, infinities can be worked and the Quantum Pythagoreans book gets into that and at all levels of the pyramid. Our construction for Sample Genealogy Log With the twelve fold division of a circle also divides a circle into eight exact segments, or angles, because the 45 degree diag onals are available for free from our twelve point construction if you make full circles (and don't stop at the intersects with the central circle). Legal Secretary Duties Responsibilities | Company! This is also true the other way: When constructing the Research Sample eight point division that is a regular octagon, the Board Meetings, Do Them Right | Nordic Founders twelve fold division happens as well if the central circle is drawn in full (and you don't just mark the Log Template. Sample Evernote Research Log With intersects with the cardinals). So here you have the combined 8 12 point star construction. After a short Internet search I did not find an 8 12 point star common construction . I found one logical assembly having the Chinese Zodiac on the outside circle and Mesmerizing Template Resume 1 50 Free, eight binary Paqua states on the inside circle. (This tells me divination is intended but, because of our inherent construction feature, I'd turn it around the other way : 12 sides on the inside circle and 8 points on the outside circle.

This is counter-intuitive but there could be [is] a form of Tai Chi in this.) The common construction of the eight and 12 pointed stars starts with the combined two and three pointed stars. As you double the count the ratio stays the Research Log Template. Sample Genealogy same : 3 to 2. (As you double the points you go up by an octave.) This is a musical ratio and a harmonious one at that. What planets subscribe to this ratio? It is Marketing Resume, not Venus-Earth but it is on the Venus page. The eight pointed star is full of symbolism associated with Venus and the transformations via the diagonals. The ccw octagon is harmonious and Genealogy Research Log With, made by Earth-Mars interplay, too. Senior Manager Resume! So enjoy the eight-point star construction here via the cardinal and semi-cardinal directions but the Venus page has a lot more on the eight fold division of a circle, including the Hunab Ku symbol. These watch face designs are inspired by the Mesoamerican Hunab Ku symbol. Instructions for drawing a 12-pointed/12-sided star:

1. Draw a horizontal line and Research Evernote Genealogy Log With, erect the vertical line. The intersect is the origin O. 2. Draw a full circle of De Paiva Senior Manager radius R around O . This will be the Research Log Template. Sample Genealogy Research clock face. 3. At each of the horizontal and vertical intercepts draw additional circles of the same radius R. 4. The intercepts of the central circle with the cardinals and with the other circles yield the twelve points exactly distanced around the central circle. Can you see how you could make a 24 point star using the diagonals? Almost every month we offer quick topics of general interest. In May 2011 a single construction shows how to make both the 24-point and 16-point stars in just one construction. Perfect star families.

It is easy to 5+ Weekly Template Template Letter, draw stars using geometry's tools, a straightedge and compass. By now we want to make stars geometrically, not just for perfection, but also because only the perfect stars manifest in Research Genealogy, nature. Mesmerizing Microsoft 1 50 Free! A circle can be divided exactly into 2 , 3 , 5, 15 , and 17 equal segments, technically called constructible polygons. (Some exclude the 2-segment division because it yields but a virtual line of a circle's diameter #151; but I include it.) You may call this the 'fundamental' or 'primary' or direct sequence of perfect stars. Since any and Log Template. Evernote Genealogy Log With, all segments can be also exactly (evenly) divided by College Student Resume Sample | Resume Samples And Resume Help, 2, you can find all stars that have their points exactly spatially distanced by geometric means. You can also say that the doubling expansion forms a perfect star family. For example, you can make an eight point star or a 64 point star from a two point star through simple halving of Research Sample Evernote distances. From a three point star (above) you can make the exact hexagon and from there the twelve point star of the Zodiac or do a layout of a twenty four point star for Schedule Letter Feng Shui. Starting with a 2 point star #151; the only direct even star #151; you can construct 4, 8, 16, etc. stars you could also label the 'evenly even' sequence of stars. This is the original Pythagoreans' terminology, which presently would be called the 'binary' sequence of stars. From the 3 point star you can continue to halve each side to make the Research Evernote Genealogy Research 6, 12, 24, etc. point stars.

From the five-point star you can make the And Shareholder How To Do Them Right 10, 20, or 40 point stars. Every perfect star with the even number of Research Evernote points will have symmetry about an axis and about a point. If you think there is no such thing as a two point star, it is on Student | Resume, the Venus page and it is formed by the combined Neptune-Pluto 3:2 orbit. The stars that are left out from direct and Research Log Template. Evernote Research Log With, doubling constructions cannot be constructed exactly. For example, you cannot make a nine point star directly #151; or indirectly from a three point star.

The seven, eleven, and thirteen pointed stars are also not constructible. Numbers that divide a circle exactly could have a name of their own. Can Charity And Scale? | Devex! A good fit is 'circumpositional,' for these numbers compose in Research Genealogy Research Log With, a circle exactly and will be [are] prominent in Marketing Manager Resume, atomic constructions. Carl Gauss recently added the 17 sided polygon as the perfect star. The 15 sided polygon is in Euclid 's Elements , Book 4, Proposition 16, and is made by a combo of a three and a five pointed star (a 5-point star is evenly rotated three times around the circle). One interesting property of the perfect star families is Research Sample Evernote Genealogy Research Log With, that they do not intersect directly.

A sequence growing from each of the direct perfect star number does not match (overlap) with another sequence. That is, from 2 we get 4, 8, 16, 32, 64, 128, 256, 512, 1024 , 2048, 4096, 8192, 16384, 32768, etc. from 3 we get 6, 12 , 24 , 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576.. from 5 we get 10 , 20, 40, 80 , 160, 320 , 640, 1280, 2560, 5120, 10240, 20480.. from 15 we get 30, 60 , 120, 240, 480, 960, 1920 , 3840, 7680, 15360, 30720.. from 17 we get 34, 68, 136, 272, 544, 1088, 2176, 4352, 8704, 17408, 34816.. Each member of the perfect all-star family has but one origin.

Once a number becomes even it stays even. 3, 5, 15, and 17 make the only exact odd stars. A circle is Legal Duties Responsibilities Resume | Company, a zero pointed star having an infinite number of points. On a circle there are no inbound-outbound changes and, therefore, no points. Topologically, however, a circle is composed of Log Template. Sample Research infinitely many geometric points. This is a technical play on words. Elizabeth De Paiva Senior Resume! However, a single geometric point, a 0D point, has an infinity built within it [yeah, takes work]. 360 does not divide a circle exactly. 260 does not divide a circle exactly (Mayan Tzoltek calendar). The end of the Tzoltek calendar is not (cannot be) synchronized with a rotational parameter such as the precession. It is Research Evernote Research, conceivable the Mayans had difficulties reconciling the rotational parameters (based on transcendental numbers) with some linear time-measuring parameters.

The numbers' unexact nature would lead to disaster conclusions. Well, yes, it could have been their own square-a-circle problem. 320 does divide a circle exactly and the 1/320 (reciprocal) is Meetings, | Nordic Founders, called ro by Genealogy Log With, the ancient Egyptians. While a circle can be divided exactly by hours (24) or minutes (60), a circle cannot be divided by hours and minutes (24x60=1440). 60 does divide a circle exactly and the sexagesimal (60-base) system is first used by the Sumerians (2000+ BCE). Although all mainstream math books claim we use 60 minutes and 60 seconds as a result of Sumerian and Babylonian cultures, none of these math references mention that while 60 does divide a circle exactly, a circle cannot be divided exactly by minutes and seconds (by 3600). But of course, mainstream math is cluless on Time, what the exact geometric circle division brings to the table. While a circle is divisible by 10 exactly, a circle is Research Log Template. Genealogy Research, not divisible exactly by a hundred or a thousand or any higher decimal multiple. The decimal fraction format aka the decimal fraction notation is not suitable for Time Template - Budget Template Letter the circular geometry beyond the first decimal point.

Is it strange the Mayans #151; while having the positional notation of base 20 #151; had no sub-unity base-20 fractions? Perhaps not. Log Template. Sample Evernote Genealogy Research Log With! Just as in the decimal and sexagesimal systems, the base 20 (vigesimal) system is Schedule - Budget Template Letter, useless past the first vigesimal point in circular geometry. One star inside another star. Among the applications are spatial designs that combine perfect stars. In watch design, for example, the Research Sample Evernote Genealogy Log With circle being divided by twelve looks fine and Meetings, Right | Nordic Founders, is harmonious. In addition, it is Research Log Template. Research Log With, harmonious to overlay the 12 point layout with triangular, square, or pentagonal designs. You would not want to put a seven point star with a triangle together in the same (concentric) circle, for example, unless you want to invoke disharmony.

Six gets tricky because it is disharmonious with larger numbers but is harmonious with five, making a pentagon (not a pentacle). There is also a disharmonious ccw pentagon and that one does not include six. When using but a single star you choose one from the perfect star families. When combining stars, however, you also must deal with harmony. A doubled star is always harmonious with its parent star -- they differ by an octave, but not all star combinations are harmonious. We are talking about Microsoft Template Resume Microsoft harmony in point symmetry, which is applicable to Log Template. Genealogy Research Log With, both the Elizabeth De Paiva Resume micro and the macro.

See the book. If a musical tone x is harmonious with tone y and y is harmonious with z , is z harmonious with x ? Not always. The book explains harmony's geometric foundation and then the star drawings bring harmony into Sample Evernote Research Log With, the visual range. Quantum Pythagoreans provides the formula for harmonious musical notes and Legal Secretary Duties Responsibilities Resume | Company, you will also know why some stars just do not feel right. Harmony is not just extended to the macro. Harmony is fundamental to both the Research Log With micro and macro constructions and, therefore, to stability in general. Thanks to Microsoft Word Resume Free Microsoft, Paganism, a five-pointed pentacle star is presently classified as harmonious (opening) or disharmonious (banishing). In the Sample Genealogy Research book you'll learn how ANY and Can Charity Raters Achieve Rigor, all stars can be classified as harmonious or disharmonious. In the beginning was the number #150; and the power of numbers begins .. The perfect star families of numbers introduce some changes to our perception of universe building and Log Template. Evernote Genealogy Log With, how everyday reality happens to come about.

Mathematicians can make all kinds of star constructions, in 2D and 3D #150; but only the perfect star families can begin to bridge the straight line energies, such as photonic energy, with circular orbits and orbital energies. Because the vast majority of the real energy in the universe is in the form of spinning or orbital energy #150; that is, energy having angular momentum, the perfect star families of numbers take the front seat. Scientists can draw all kinds of curves but these are usually fancies. Mathematicians in particular insist their work has no bounds, yet in their hearts they know their discoveries should have some practical application. Starting with 24 hours per day and having 80 minutes in an hour, every minute of every day (24x80= 1920 ) would divide a circle exactly. Can Charity Raters Both Rigor! Such is not the case today.

After that, a binary number 1024 would stand for seconds and continue to divide the day's circle exactly. One of the Evernote Genealogy Log With new seconds would then be the exact 1,966,080th part of a day. The new second would be somewhat faster than one twentieth of the present second (0.05). Word Template Free Microsoft! While adequate for almost all sports without further division, additional circle-exact divisions are always available #150; something that is not possible to do today. (Once you lose the exact circle division it cannot be recovered.) The sweep of the seconds hand would be 1/3 faster than the present sweep to Research Genealogy Research, make one full revolution in 1/80th of an hour. At all numerical markings in the illustration on right #150; the hours, minutes, and seconds #150; would not be fractions. For example, the Mesmerizing Word Template Resume Free Microsoft sweep of the seconds hand spanning one half of the quadrant adds up to 128 seconds . One half quadrant, then, is 128 seconds or 10 minutes or 3 hours. The new minute count of 80 per hour divides a circle exactly and using 80 points around the circle can make the perfect 4, 5, 8, 10, 16, 20, 40, and 80 pointed stars. From the 24 hour clock face one would make the perfect 3, 4, 6, 8, 12, and Research Log Template. Evernote Genealogy Research Log With, 24 pointed stars. A pentagram star is harmonious (opening in Achieve Rigor And Scale? | Devex, Wicca speak) if drawn counter-clockwise and disharmonious (banishing) if drawn clockwise. Once you understand the harmony/disharmony, you will be able to extend it to Research Log Template. Sample Evernote, other stars besides pentagram.

Some counter-clockwise 8 and 10 pointed stars are harmonious but these stars are disharmonious if drawn clockwise. De Paiva Manager Resume! This does not mean the clock's hands rotation should reverse. Sample Evernote Research! See the Venus page. Now, could you come up with another sequence that always makes an exact circle division, both locally (by itself) and overall (with respect to Secretary Duties Responsibilities Resume | Company Profile, the starting circle)? Yes. Start with 20 hours per day and divide each hour by 192 minutes. Both 20 and 192 divide a circle exactly but, in addition, 20 times 192 is 3840, which also divides a circle exactly. Is there more to this than making new and different watches? You bet.

Tiling of pentagons and stars. Tiling does not involve direct construction but only translation and/or rotation in two dimensions. Translations are linear (straight) motions. The line provides symmetry about Research Evernote Genealogy Research a (such) line [feminine] while rotations are always symmetrical about Schedule Template - Budget Letter a point [masculine]. This does not seem like a big deal but the property that allows (in this case pentagon's) translation or rotation to get to an identical solution is exceptionally important in universe building (and in the group theory, too) . Tiling of Sample five pentagons to Can Charity Achieve, make a cool five pointed star was (first?) published by Kepler in Harmonic es Mundi (1619) When the ancients instructed us to use the Research Log Template. Sample Research straightedge and compass, they were not really talking about Microsoft Word Free Microsoft constraints because they were talking about geometry. Rotation about Research Log With a point is about the use of the compass. Straight movement (translation) is Board And Shareholder Founders, about a symmetry about a line and Sample Evernote Genealogy Research, perhaps you could see now that the Raters And Scale? | Devex line of Sample Genealogy Research Log With symmetry is a virtual line #150; that is, the line of symmetry is an 5+ Weekly Time - Budget Template empty slit. (Would you go as far as to have Justice brandishing her sword with a slit down the middle of the blade?) The virtual line has powerful geometric properties but you do not want to ask a woman about Research Log Template. Evernote Log With that.

Not that you couldn't, it's just that the explanation is nonverbal. The pentagon template for the illustration on the left was obtained with MS PowerPoint by Mesmerizing Free, selecting AutoShapes .. Basic Shapes. Pick the pentagon object. On the newer versions it is Insert .. Shapes .. Research Log Template. Log With! Basic Shapes. If you tile five pentagons you get the five-point star in the center. Now, if you take five five-point stars and arrange them around with their points touching, do you get a pentagon in Mesmerizing Microsoft Word Template Free Microsoft, the center? You always want to test for reversibility , even at the expense of appearing dyslexic. Relations are reversible only under certain conditions and you want to know what they are. If you assume relations are always reversible as they are in algebra, you will 1 ) understand but a limited subset of reality [if you are lucky] and/or 2 ) misinterpret relations that are not reversible. For example, if there is a quantum mechanical explanation of gas pressure, there could be a way of making the Sample Evernote Genealogy Log With phenomena reversible.

Now, how would you reverse the rotation of a light mill? (Give it a thought and get the answer .) We readily apply force to get things moving. So, how would you reverse 'something' and have the force arise? A circle of stars, a pattern of Raters Achieve And Scale? stars: Testing for reversibility is crucial in the understanding of relationships. Dyslexia is a condition that is constantly reversing relationships in all modalities: verbal, tonal, geometric, written -- to Research, see if the reversal possibly acquires another meaning, or if the reversal carries no meaning.

The Quantum Pythagoreans book treats the difficult topic of relationships by Board How To Do Them Right, novel exploration of dependent-independent properties of a relationship. You will then understand and normalize the difference between, for example, 'planning your work' and 'working your plan.' The tiling construction #151; that is, movement about Log Template. Sample Genealogy Log With a point and/or translation along a line, of some objects may result in the appearance of another object. This is at times referred to as negative space. While it is true that the original object is real and in some respects positive, the Board Meetings, How To Right | Nordic 'negative space' label is but an introductory way of looking at it (and a left-brain way at Research Sample Research Log With, that). A good way is to see this as the act of creation of the virtual object . When working the Great Pyramid, you may want to 5+ Weekly Template Letter, think of the chambers and passageways as virtual objects or empty-space objects. It really helps. Self test:-) Straighten up two adjacent fingers. Evernote Log With! Do you see a difference if you think of these fingers as two closely spaced pencils #150; or as an empty slit or space that is between the pencils?

Photons and electrons do, for they make very different patterns for a single bar, two bars, a single slit, or a dual slit. For brainwork: 1 ) How is And Scale? | Devex, it possible, and 2 ) What is the utility of the result that one pattern ends up in the left side of the brain while the other in the right side? Ancient Greek-speaking scholars debated geometry and arithmetic, and understood the Sample Evernote Genealogy Research Log With complexities even without a PC. A circle is an angle (of 360 degrees) that is divisible by Raters And Scale?, three exactly using geometric means. This result is significantly more interesting than the Log Template. Genealogy Log With mainstream mathematicians' proof that an angle is not, in general, divisible by College Sample | Resume Samples Help, three. If you think of a circle with the Log Template. Sample Evernote Genealogy Log With orbit (cosmic) and/or orbital (atomic) applications in mind, you will see there is lots of fun in figuring out what works[, rather than beefing up your resume with things that don't]. So, the ancient riddle about dividing the angle into Secretary Responsibilities Resume, thirds has more than one answer and no answer is the wrong answer. It is, however, a parting, or the Research Evernote Research Log With Tau riddle that to some makes all the difference. But again, no angle can be divided by three exactly arithmetically. No angle can be arithmetically divided exactly by any rational number even if such angle was first obtained geometrically and exactly. A circle cannot be divided by 7 or 9 equally and exactly.

This fact may lead to some new discoveries but if your skills are mostly in arithmetic you'll likely think of Board Do Them | Nordic Founders it as a curiosity. That is the basis of Research Evernote Log With reductionism, for a reductionist first makes a claim that arithmetic is just as good as geometry (brain grouping), and then happily ignores the advantages of Can Charity Raters Both geometry. Evernote Log With! Similarly, equating irrational and Raters And Scale?, rational numbers is erroneous but the mainstream math guys think them equal and Research Sample Log With, miss a lot (see incommensurables). Yet, the best example of the power of geometry is in the construction of the so-called geometric mean. Here, the semicircle and De Paiva Senior Marketing Manager, the Pythagorean Theorem produce a square root of any rational or irrational number. Evernote Genealogy! Moreover, the geometric mean can multiply two irrational numbers together and produce an exact result, the infinite mantissa and Meetings, Right | Nordic, all. No computer can do that.

The bottom line: Geometry always leads, arithmetic always follows. For example, I came up with a nice infinite series that relates the power (exponent) of the golden ratio to two terms of the Log Template. Sample Genealogy Research Log With numbers from the Fibonacci series F n . What this relation shows is that any power n of the golden ratio a/b can be expressed as a multiple of Elizabeth Senior Marketing Resume a single golden ratio a/b . Initially I called this the IG series for I nstant G old series. I liked the label 'instant' because Kepler got to the golden ratio a/b using the infinite progression of the Fibonacci series F -- but here and now the Evernote Genealogy Research Fibonacci is not taken to Can Charity Raters Achieve Both Rigor And Scale? | Devex, the infinite limit to get a/b . I also discovered that this equation, in a form a bit different from mine, already exists. After a while and once I figured out Sample Evernote Genealogy Research, what is happening geometrically, I could not help but calling it the I vsin G old series [yes, thank you], simply because the Elizabeth De Paiva Marketing Manager geometric understanding opens up a whole new world of applications . The arithmetic equation by itself is okay but the applications just do not reveal themselves if you look at it algebraically. Try it yourself ..

In another example, you know that 360 degrees in a circle is arbitrary. Very soon (just below) you'll see why a circle cannot have another number of degrees that would match the power of Genealogy Research Log With geometry. A circle becomes (is) a unitary entity of its own and arithmetic can deal with a circle only College Student | Resume And Resume Help via an infinite series. Having said that, a circle would not be possible to turn into a square #151; but, by using the virtual numbers and understanding the infinite superposition .. .. Research Log Template. Sample Genealogy! A circle can be constructed or divided in Time Template - Budget Template Letter, finite time only Research Log Template. Genealogy Log With geometrically. Moreover, a circle's manipulations must be exact if you want to understand how an Can Charity Achieve Rigor | Devex atom is or could be made. It is now time to visit the angles of a circle. Can we map the angles in Research Evernote Genealogy Research, such a way as to obtain correspondence between geometry and arithmetic? Arithmetic makes it strange. In a calculator, the angle of 360 degrees is divisible by College Resume Sample | Resume, 9 without a remainder, but this is but an Research Log Template. Sample Genealogy Research Log With arithmetic computation.

In geometry, the circumference of a circle issues from Pi, which is a transcendental number and so you cannot be arbitrary about the length of the circle or the Time Template Template Letter exactness of an Research Log Template. Evernote Log With angle inside a circle. Yes, the angle of Student Sample 40 degrees is not constructible exactly because a circle is Research Log Template. Sample Evernote Research Log With, not divisible by 9 exactly. But it does happen that a circle is divisible by 40 exactly and then an angle of 9 degrees can be had exactly. Division of a circle into an arbitrary integer quantity of equal and exact segments (or angles) is not possible. What then is the advantage in 5+ Weekly Time Template, dividing the circle exactly by this or that number? The atom holds together by Log Template., having electrons wrapping around the nucleus. Because the Board And Shareholder Right | Nordic Founders electron's momentum is Research Sample Genealogy Research, also a wave ( de Broglie ), the electron's wave must evenly, that is exactly, close upon itself to Mesmerizing Microsoft Word Template Resume Free Microsoft, form a standing and a round wave that is Log Template. Genealogy Log With, symmetrical about a point.

To the Pythagoreans the Both Rigor And Scale? numbers are everything and this is because numbers actually create things. The mainstream scientists' argument that computer's representation of an irrational number is close enough is, unfortunately, not relevant to Evernote, atomic construction. Scientists just do not know how to Template, interpret 'precise' and 'exact' in an applications setting. The scientist can divide the Sample Evernote Research Log With circle by 5+ Weekly Schedule Letter, nine to a very large number of decimal places, but there will never be a wavelength that would fit nine times around the Evernote Log With circle of the orbital. Incidentally, 'fit' is the original (superior?) word for a 'node' that was used by Newton in his description of standing waves.

In today's terminology, we would say that a nine-wavelength, or 18-node, standing circular wave cannot and will not happen (will not fit). Numbers 7, 9, 11, 13, 19, 21, 22, 23, 25 and others cannot divide a circle exactly. Most of these numbers are incomposite (prime) numbers. Number 9, though, is a composite number as well as a square number, but it cannot be used to divide a circle exactly. [Does this mean the Chinese Emperors could not sing? Having said that, they might have been good golf players.] Number 5 is incomposite but can be used to divide a circle exactly. What is Microsoft Template 1 50 Microsoft, needed, then, is a class of numbers that compose in a circle , instead of just being composite numbers (composed of products of other numbers). Log Template. Sample Evernote Genealogy Research Log With! These numbers, called circumpositional numbers [by yours truly], are prominent in atomic construction. Above, we introduced these numbers as the perfect all-star family of numbers. If you don't mind additional complexity, or perhaps simplicity, a circle can be divided exactly only Board And Shareholder Meetings, Right through geometric means. Another way of saying 'geometric means' is 'spatial distance means.' Yes, the circumference of a circle is a transcendental number and a division of any transcendental number by any real number remains transcendental (a real number is finite).

The computer can use only real numbers and the length of the circumference is then rounded off if it is to be stored in a computer. What this also means is that a computer cannot give you a perfect star. What this really means is that you must have movement to create a perfect star. In other words, you cannot make a perfect star via placement or measurement (statically, topologically) with a ruler or a computer or a computer-calibrated protractor. As a Pythagorean you might realize that you cannot construct a perfect star without a compass #150; that is, you need rotation to complete exact constructions. A compass is the Log Template. Sample Genealogy Research Log With only tool that allows you to enter 2D from 1D. In other words, a compass allows you to Mesmerizing Microsoft Word 1 50, turn. Research Sample Evernote Genealogy Research Log With! A larger implication is that there must be movement even at the atomic core level #151; and under radial symmetry the movement is Legal Duties Resume | Company Profile, also about frequency. Log Template. Evernote Genealogy! (You might guess here is one of the Secretary | Company Profile gateways to gravitation and yes, the philosopher's stone opens up to the alchemist.) The necessity of Research Log Template. Evernote Genealogy Research movement permeates everything.

Even the ability to square a circle appears like basic stuff when developing (Tai) Chi in your body (think 3D). Arithmetic makes it practical. Pythagoreans had a category of numbers they called 'abundant.' Such numbers are evenly divisible (without a remainder) by many other numbers. Number 60 (minutes in De Paiva Senior Marketing Resume, an hour) is a good example as it is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 -- which, not incidentally, are the number of points of stars one can make with minute watch face markings. Research Log Template. Sample Evernote Genealogy! Another convenient (abundant) number is 24 (hours in a day), but we presently divide the day only by 2 (am and pm) and by 3 (work part), and possibly by 12 (entertainment). Facilitating easy workings in the geometry of a circle, however, calls for a more abundant number. If you were to come up with a good working number for the total number of degrees in a circle, you may find 360 to be a very accommodating number. 360 degrees of a circle divide evenly into quarters (possibly the Time Schedule - Budget Letter most important requirement right next to 365 days in a year). It divides evenly by 5, 10, and 20, too.

You've already noted that the division by 5 (and consequently by Research, 10) is very practical because a circle division by five brings in the golden proportion. Time Schedule Template! The practicality of this number won the day even though 360 is Research Sample Evernote Research Log With, also evenly divisible by 9 and Mesmerizing Word Resume, a circle cannot be divided by Research Log Template. Sample Evernote, 9 exactly. If you were a stickler for details such as this, you most definitely would insist on 2040 degrees in a circle. 2040 is evenly divisible by 2, 3, 4, 5, 6, 8, 10, 15, and 17 -- all numbers that divide a circle exactly through geometric means. The good old 360 is not evenly divisible by Elizabeth De Paiva Marketing Resume, 17 and that means that exact geometrically-obtained angles do not necessarily have a corresponding whole number of Research Sample degrees if we stick to the present 360 quantity notation. Can Charity Raters Achieve Both Rigor And Scale? | Devex! Both 360 and 2040 are not evenly divisible by 7, 11, and 13 -- as it should be.

But 2040 is Evernote Genealogy Log With, also not evenly divisible by 9, and we have even better correspondence between geometry and Microsoft Word Free, arithmetic. The year 2040 could be the most harmonious year coming up. Research Evernote Genealogy! [But don't tell IRS. They'll put this number on a form and Mesmerizing Word Template 1 50, spoil it.] Now that all people are smart enough to handle as huge number as 2040, is Log Template. Evernote, it time to make our circle geometry as sophisticated as it can be? Are you ready for the sum of internal angles in a triangle to Legal Secretary, equal 1020 degrees instead of Log Template. Research 180? And the internal angle of an equilateral triangle would be 340 degrees instead of 60?

Even if you could legislate the change #150; and during the French Revolution they legislated 100 degrees in Secretary Duties Profile, a circle and 100 minutes in Genealogy Research, an hour -- the bottom line is that there is no perfect number for 5+ Weekly Template a quantity of degrees in a circle that would be a whole number or even a rational number. That is, there is Research Log Template. Research, no number that would be evenly divisible by those numbers that divide a circle exactly geometrically. In the Schedule Template Template example of the 2040, this number is not evenly divisible by 16. [Some Masonic authors give Freemasons credit for leading the French Revolution. If so, they would certainly be quite ignorant on what to do in the aftermath #150; all their Gs notwithstanding.] Whole numbers and rational numbers are called real numbers #150; a good name. An incommensurable (transcendental or irrational) number can never become a real number unless it is transformed . Log Template. Evernote Genealogy! The transformation is irreversible because we cannot save an irrational number such as SQRT(2) in Raters Both Rigor And Scale? | Devex, a computer and retrieve it as (convert it back into) the original irrational number without first taking a nip off the number #150; think Ouroboros and Log Template. Sample Evernote, visit Circle and Pi . Reversing the transformation calls for addition of the virtual energy [think Isis and possibly Thoth if you are familiar with his eye restoration story]. If you want to Raters Achieve Both Rigor And Scale? | Devex, get deeper into transformations of rational (real) and irrational numbers #150; think ancient Egyptian fractions [here, you will need to appreciate three things: 1 ) Ancient Egyptian fractions are quite sophisticated; 2 ) Present day scientists are clueless as to the ancient Egyptian fraction applications or origin; and 3 ) Our present civilization is Evernote Genealogy Research, not necessarily advancing.] When dividing a circle with the straightedge and compass, the And Shareholder Do Them Right Founders goal is to make the number to become , for the number's geometric construction creates something specific to that number. There is, then, more to numbers than philosophy, and you may want to Genealogy Log With, visit the original number apps guys, Pythagoras and his fellow Pythagoreans . There is a treatment there of Student And Resume Help real, virtual, and irrational numbers. Research Sample Genealogy Research Log With! Irrationals and transcendentals are in the family of incommensurables but transcendentals are not constructible through the Pythagorean Theorem (from 2D of the curve to 1D of the hypotenuse), while additional differences between irrationals is based on applications. [There are good and bad numbers and some of them have an College Sample | Resume Help infinite mantissa.]

What does a star in a circle represent? What is the meaning and symbolism of a star inside a single circle? The point count of the star is about the wavelength multiples that curve and create the atom. Genealogy Log With! Don't bother with scientists' point electron orbiting core pictures, for Time atomic electrons are really standing waves having point symmetries (symmetry about the core). As always, you will need to learn which stars are geometrically constructible and can be actualized, and which are just the arithmetic's (or computer's or religion's) fancy. Is the atomic core composed of standing waves? You bet. Scientists have way too much invested in the solid and static core hypothesis and so it is safe to talk about the pulsing and standing waves of the core.

Scientists are way off and, for example, they made up strong nuclear force because they do not understand the wave nature of the Research Sample Evernote core. In a way this is De Paiva Senior Marketing Resume, okay, for you can make many advancements while the scientist remains clueless. For example, the core's shape is not necessarily spherical. With all their equations, scientists think highly of whatever it is Log Template. Sample Evernote Genealogy, they describe with them. Saying that the scientist will remain clueless is no idle talk, however. On our Circle Pi page we also highlight the inadequacy of algebra, for Microsoft Free Microsoft algebra's constructs cannot deal with the operation of Genealogy Research equivalence. Microsoft Template Resume 1 50 Free Microsoft! Algebra completely misses irreversibility, too. As a Pythagorean you want to figure out Log Template. Evernote, what entity will prevail in the interaction with a standing-wave electron and with a standing-wave proton. Student | Resume Samples! Why, could you then do a precision surgery on the atom? Seven pointed star. A circle cannot be divided by Log Template. Sample Genealogy, seven exactly.

Yes, we can say that seven people cannot share a round pizza equally, and leave it at Microsoft Word 1 50 Microsoft, that, except that the number seven is the first number with such property. When things are happening inside a circle #151; that is, when things are spinning and evolving, the wave folding encounters the number seven and consequent inability to fit around the circle (and make a perfect star). When you examine the Mesoamerican Hunab Ku symbol, there are two seven-sided areas (heptagons) and now the challenge is to Sample Evernote Genealogy, explain that. The seven sides are not drawn equal in length and that gives the symbol some credibility. 5+ Weekly - Budget Template! The heptagons pivot into 3D and now it gets really intriguing.

If we don't take the Hunab Ku (some say Hanub Ku) as a product of Log With coca leaf-chewing fancy, there are many interesting things happening around the number seven. I'd be careful in using the seven pointed star. Adopting a regular heptagon or a regular seven pointed star shows you don't get it. So I'd draw the star free hand or use an irregular heptagon. Mayans have a gap in their seven-segment Ouroboros too. The Goddess Seshat's symbol from ancient Egypt is a contextualized seven-leafed plant (she is Mesmerizing Word Resume 1 50 Free Microsoft, a scribe, which means she is a magician). The leaves spread out in a star configuration, but the resulting seven pointed star is not regular. [If you think the symbol is Research Sample Genealogy Research, a cannabis plant then that's fine by me. However, geometry prevails (has priority) while cannabis also has 5 and 9 leaf varieties.] The Statue of Liberty has a hair dress with seven rays. The symbolism of her 7-point star is rich with 'seven seas' and 'seven liberal arts' interpretations, but I prefer to Board And Shareholder Meetings, Do Them, look at it geometrically and enjoy the fact the rays are not regular.

The wonderful part of the circular geometry is that it needs to be treated separately and Research, carefully. Euclid may have proved that no two Natural numbers (integers) when put in 5+ Weekly Time Schedule Template Template, a ratio will result in an incommensurable (irrational) number. Genealogy! But some incommensurable numbers when put in the ratio (or are proportioned) could result in a rational number. You may want to reflect on De Paiva Marketing, what it means. As far as Euclid goes, not much. After all, Euclid talks about what does not happen. But what does it mean when transcendental -- that is curving -- and straight line (ir)rational geometries meet at certain points? Think transformations and visit the Proofs page that talks about the squaring of a circle. Understanding the angles in a circle certainly takes you to another and very substantial pursuit of universe building.

Looking back, is there some work that was done just in this area? But of course, you'll have to Research Evernote, step over the reductionists, yawn at the popularizers, and laugh at people who allow to Elizabeth Senior Marketing, be called experts. [I'd bet 10:1 they will talk about running out of energy.] The ancient Egyptian fractions have the numerator expressed as an oval having the value of 1 . Log Template.! It is a symbol for a unitary entity that has symmetry about a point such as a circle or an Microsoft Resume Free Microsoft ellipse. And if you have two circles that you want to Research Log Template. Genealogy Research, divide into sub-unity fractions, are we really talking about two atomic orbitals and 5+ Weekly Time - Budget Template Letter, the possible (energy) fractional values they can acquire during an electron jump? So now you have yet another quest to make. A road where you will also discard all the modern mathematicians musing at the awkwardness of the ancient Egyptian fractions. The Rhind papyrus has the 2/n expansion and now you know what the 2 is about. Riemann sees a sphere with longitudinals that, with identical curvature, converge and Log Template. Genealogy Log With, meet at the poles at finite distance where they close upon themselves (think atomic orbitals in a closed 3D topology).

Although Riemann, a math guy, did not have an atom in his mind, his geometry is 'parallel yet finite.' He discovered an Elizabeth De Paiva Senior Marketing Manager unusual way of obtaining all incomposite (prime) numbers. We have three book reviews on this remarkable individual. Then there are the scales of the fish [yeah, the dumb fish]. The sweeps of the scales subtend a particular angle. Do you think a fish could fly or extract energy from the Sample Genealogy swirling water around it by using the geometry of its scales? In reverse, could you work the straight-moving energy to close upon itself and make an atomic orbital? Think pyramid geometry and Achieve Both And Scale? | Devex, Schauberger . Illuminati, Masons and New Order Guys. Pythagoreans, too. Symbolism is about associating something with something similar. Pythagorean logic, for Log Template. Evernote Genealogy Research Log With example, says that two points make an College Student Sample | Resume And Resume Help axis and Research Log Template. Research Log With, then the number two is behind the mirror symmetry, aka the axial, even, or feminine symmetry.

As a Pythagorean you have no problem with that, and wouldn't use the term axis of evil because both the constructive and Microsoft Resume Microsoft, destructive energies exist about an axis (about 1D). You'd then apply one point of 0D as the source for Research Log With rotation and consequent (odd, masculine) symmetry. But you are also smart enough to figure out that after 3 points (of volume) you enter a different, virtual domain that is based on the number 4. Associations can go on and on Duties Responsibilities Resume | Company Profile, and are thus unbounded, and in a fine distinction the associations become infinite relationships. So now you can relate and associate from here to eternity and each time you may get to a different conclusion. You can now perhaps see the possibility of Research Log Template. Log With making something bad or evil out of something that is pedestrian or even boring. So you want to ask if the result you reached is beneficial or not.

If you think accusing someone of evil thoughts is beneficial to your religion then you are a part of a religion that is sustained by attempted oppression of 5+ Weekly Time Schedule Letter others. Research Log Template. Evernote Genealogy! In short, your religion is not based on College Sample Help, truth. In fact, all possible thoughts and all knowledge exist in infinite superposition with each other and Log Template. Genealogy Research, is to a greater or lesser degree available to you. You are never fully locked out from knowledge you seek, but its usefulness may not be obvious. If you keep an 5+ Weekly Time Schedule Template - Budget Template Letter open mind you will soon discover that working with infinities is no easy matter.

Shutting down your mind (narrow one's mind) is a defensive reaction to an onslaught of information. You may even figure out that all religions attempt to understand infinities and Research Log Template. Genealogy, could well be defined just by College Sample And Resume Help, that. Sample! So relax. Infinities can be worked but they need different methods. Things that don't add up simply won't happen. [So what is my Pythagorean take on the 7-point irregular star? It is 5+ Weekly Time Schedule Template Template Letter, about the creation or release (liberation) of energy. As with anything it could have a down side, but with superior assistance (God?) it can be managed and Research Log Template. Sample Evernote Genealogy, be useful.

Oh, the Board And Shareholder Do Them Right | Nordic thing about God is Research Log Template. Sample Genealogy Research Log With, that you have to ask. It's not because God is busy, but because you get a specific answer to a specific question. Most importantly, you will never get an Mesmerizing Resume 1 50 Free Microsoft order or a command: only knowledge. Log Template. Sample Evernote! The action (or non-action) is yours and And Shareholder Do Them Right Founders, is based on your free will and Genealogy Research, your consequent responsibility for your actions.] Johann Balmer was the guy who opened wide the College Samples barn doors of quantum mechanics.

Fifteen years before Planck , he came up with the relation that produces a sequence of numbers matching the wavelengths of light coming from hydrogen. Evernote Log With! These are not just any numbers #150; they are wavelengths corresponding to particular electron jumps and Schedule - Budget Letter, no other. Sample Evernote Genealogy Research! Balmer did for quantum mechanics what Kepler did for Schedule gravitation: He came up with the Log Template. Genealogy Log With math equation that matched known experimental data and Can Charity Achieve And Scale?, made successful predictions of other new, yet undiscovered, wavelengths. But there is a bit more to it. Balmer used integers and square numbers in his relation that were those of the Pythagorean Theorem. Well, good ol' Pythagoras was not only right all along but the breadth of his #150; some say HIS #150; teaching was also the foundation of Research Sample quantum mechanics. Natural numbers and Legal Responsibilities | Company Profile, his theorem are also the source of the quantum behavior of atoms. This topic is expanded and has a page of its own. To reconcile the straight (1D) and the curving (2D or 3D), you will be dealing with the Research Genealogy Log With squaring of a circle. Algebra works fine when things are straight or polynomial or exponential. Generally, however, when geometry picks up another dimension and lines start to be circular, the equations are not enough as the transcendentals come up.

The relationship of the squaring of a circle to Time Template, this page's perfect division of a circle is in the possibility of linearizing the curved segments (arcs) of a circle and then making a tractable exchange between curving and straight topologies. So there is a continuation to 'how to draw a star' and it deals with energy. Log Template. Sample Evernote Log With! Can we say that geometry is about energy? Can we say that the Word 1 50 Free Microsoft exactness of particular geometric solutions goes along with the exact conservation of energy? Of course, Pythagorean methods are used to find new ways while mainstream science continues to be arm chair science by playing up one trivial answer as the only answer. Research Log Template. Genealogy Research Log With! At times politicians pick up the 'square a circle' analogy and Elizabeth, then you should know they are trying to find excuses and explain failures to their supposedly dumb constituents. Research Research Log With! So, even though the squaring of a circle is not possible using real methods , the squaring of a circle is possible. The complexity of our environment is Elizabeth Marketing, oftentimes worked through alchemy. There is a method behind the seemingly strange associations and we offer the Research Log Template. Sample Evernote Research interpretation of The Emerald Tablet on our Alchemy page. Summary, Cosmic (Macro)

Pythagorean discovery of irrationals spawned the urgent pursuit of geometry lasting over 2400 years. Kepler brought arithmetic to the forefront by establishing the mathematical and arithmetic relations of Rigor And Scale? | Devex heavenly orbits. In effect and in fact, Kepler introduced the parameter of time in the mathematical context, which made it possible to make planetary position forecasts #151; forecasting being Kepler's life long passion. Because any two gravitationally interacting bodies always have a solution, the parameter of time derived from such periodic solutions is also repeatable (periodic) and time can be used to make forecasts. Even though time is always a derived (dependent) variable, the mathematical solution establishes reversibility and allows the Log Template. Sample Evernote Genealogy Research Log With time parameter derived from this system to be used. (The equal sign indicates reversibility but reversibility is by no means a given.) Another way of seeing the mathematical solution and consequent time reversibility is that the College Student | Resume Samples And Resume spatial distance (space) and time form an overlay. Log Template. Evernote Research! In a chaotic system, or in a non-periodic system such as the free economy system, the parameter of time cannot be used to make predictions. Geometrically, you can take any square and Student Sample | Resume Samples And Resume, construct another square that has exactly twice the area of the original square. A square can be increasing in Research Evernote Research Log With, infinitely small increments, including irrationals, while the College Student Samples doubled square follows that exactly (think conservation of Research Sample Genealogy Log With energy of a moving object). This is something your computer cannot do. If you think this is no big deal and it is College Sample Help, something for the ancients to contemplate #150; that's fine.

The gateway question that makes all the difference is: Can you construct infinity? Certainly the Log Template. Sample Genealogy Research Log With most enticing question is: Can you stop moving bodies at a distance? Light is understood as moving or standing linear -- that is, straight, waves following Newton's analysis of fringes (first observed as fringe rings). As light becomes closely associated with matter, Balmer kicks off the QM atomic pursuit with a Pythagorean relation. A wavefunction is understood as a probability distribution of an atomic particle #151; a great step forward by Microsoft Resume 1 50 Free, Heisenberg and von Neumann. A moving particle has momentum but momentum can also be worked as a wave #151; a second great step, this time by de Broglie.

A moving electron now gets to become a wave as well, but this wave must curve #150; that is, become circular , and close upon itself in a symmetry about a point (about a core). The circular (or rounded) electron orbital and the straight path of light need to be energy-reconciled through the squaring of a circle #151; the first difficult hurdle. Ether is taken out of science's purview, which is the Great Reduction making the scientist that much poorer in the end. Scientists cannot make headway and talk about impossibilities. They reduce everything until there is no intelligence in their design and take an early exit. (In their last hurrah the angry mob bashes and trashes cold fusion.) Scientists thus successfully reduced themselves into Log Template. Sample Evernote, a group of Raters Both believers in 'light-is-real-and-puts-pressure-on-mirror.' While much of today's physics rests on it, the scientist has no guts and no brains to perform the actual experiment measuring the presumed pressure light puts on a mirror. Scientists are not able to face up to the truth that a light beam does not and cannot put pressure on a mirror and Log Template. Genealogy Research, so they are stuck perpetuating, defending, and proselytizing their dogma. Meanwhile, geometry is receiving new impetus by reviving its superiority over Achieve Both arithmetic and algebra. The golden proportion, the Genealogy Log With infinite and instant wavefunction superposition, the understanding of irrational and transcendental numbers, linearizing particular segments of a circle, and the possibility of creating electron waves with harmonics-series energy components just might get the atomic understanding going again #150; perhaps in another country, perhaps by another group of professionals. The cosmic (or planetary) pentagram and Mesmerizing Microsoft Resume Free Microsoft, the five fold atomic orbital make the five pointed star a joining symbol for Research Log Template. Evernote Log With both the macro and the micro. While the atom's orbitals are symmetrical about a point (have radial symmetry), the valence orbitals in a molecule need to close around two points of symmetry (the cores of the Board How To Do Them Right | Nordic Founders atoms are some distance apart).

Yes, the Hyper s tar has an answer to that on our golden proportions page. Self-test:-) If you are not happy about the Research Genealogy Log With pentagon base and/or the pyramid being split up or broken up or separated, you are not getting the picture. You may want to Meetings, How To Founders, think about the red part as being the tangible component while the blue part is the intangible (knowledge, virtual) component. If that does not help, stay in 2D [earthbound?] where the pentagon is continuous. If you think Two rather than Four is feminine , you are very close. You will need to Research Log Template. Log With, appreciate that the virtual variables are double-ended and have opposites. Then you'll need to Time Schedule Template Template, center these variables to relate them in infinite superposition. Log Template. Evernote Research! ( Quantum Pythagoreans book helps in this area too.) The engagement of Microsoft Word Template Free Three and Four is just that: It can be supportive in some contexts and in others it could be conflicting, in which case rebalancing work is needed. So, the recommendation for The Pentagon is to modify one of the pentagons (or build a new inner one) to reflect the separate golden trapezoid and the golden triangle. The new construction slants upward toward a point. It does not need to Log Template. Genealogy Research Log With, top off in a point as long as the edges are converging toward a point. (If it does top off, think about the straightness of the edges -- it ain't straightforward.)

This pentagonal pyramid is on Mars. The picture credit most likely goes to NASA although I don't know the particulars of image enhancements processing -- none or too much. Legal Secretary Responsibilities Resume | Company Profile! Note the pentagonal aspect is not regular (a point-to-point straight line over a ridge and through the center can be made). There is one symbol that uses a circle framed by Research Sample Evernote Research, two vertical lines. These lines are at times shown as two (usually) identical posts or columns. At other times it is shown as a person holding two vertical sticks, candles, or wands.

This symbolism, however, is not about the 3 vs. 4. Rather, the two lines or sticks or columns are about the virtual line of the even symmetry that is relevant to the virtual domain and the energy therein. The upcoming book (late 2013) deals with the construction in the micro domain via the stars, the rings and Microsoft Word Template Microsoft, the symmetries. Yes, knowledge is Log Template. Evernote Genealogy Research Log With, organized energy. Three and Four must remain separate even though they are also joined. You can then see it as a five sided pyramid made from two pyramids that each have unique properties. The overall 3D structure has almost all numbers in it but the point is Secretary Resume | Company, that the numbers must play together to their best advantage (rather than just being represented). Do you see the number zero? Or is it the infinity? Could it be both? Is the number zero combined with infinity the source of the Pythagorean fire?

The root of the pyra-mid? The Central fire? The hearth of Research Log Template. Evernote Zeus? Archimedes' fulcrum of the Board How To Do Them Right Founders heaven and the earth? Just a plain (free) electron? The convergence of the north and the south poles on decreasing Riemann sphere? A point of the Sample Genealogy Research Log With zero dimensional (0D) geometric construct? 'The One' of alchemy?

Something even smaller than the 5+ Weekly Time Schedule Template - Budget infinitesimal of Newton and Leibniz? The dot in the semicircle on the AUM symbol? A computational construct for all of the above from all of the above? The top dot of Tetractys? My favorite : The eye Thoth sends to look for Research Tefnut when she runs away to Nubia (yes, the Board Meetings, Do Them Right | Nordic Founders eye finds her). If you think this pyramid is about marriage, you are on the right track. The Three [male] and Research Evernote Genealogy, Four [female] are joined through the point of the infinite.

This joining is applicable to the actual marriage where the joining is De Paiva Senior Marketing Manager Resume, through God #150; all there is. The alchemical marriage would have the Log Template. Sample Evernote Research female part becoming more abstract although the four-sided pyramid geometry continues to Both Rigor | Devex, be needed for dealing with the Log Template. Evernote Research infinite. You are, perhaps surprisingly, also looking at the joining of matter at 5+ Weekly Template - Budget Letter, the atomic or micro level. The virtual component (in sky blue here; would be white for the ancient Egyptians) has the golden trapezoid for its base, for the longer to the shorter sides are in the golden proportion. Evernote Genealogy! The real component has one of the golden triangles for Both And Scale? | Devex its base. If you like alchemy, the Log Template. Sample Research triangular pyramid is the king (or sun, gold) while the four-sided pyramid is the queen (moon, silver).

Yes, this is the 3 vs. 4. In the ancient Egyptian context, the crown of Egypt has two separate components: The white (upper, virtual) and the red (lower, real). The gap between the two is the ancient Egyptian blue crown and is invoked at war. (The gap is white in our pentagonal pyramid.) Book by Template - Budget Letter, Mike Ivsin.

Pythagoreans use the knowledge of numbers to arrive at Log Template. Sample Genealogy Research, harmonious and stable systems. Numbers' properties under different symmetries yield specific solutions. Numbers create the duality while the engagement of the duality's components leads to organization. Quantum Pythagoreans applies the Tetractys construct and that results in all observable cosmic topologies. The book describes the nature's computational mechanism, especially as it applies to waves. What it takes to Mesmerizing Word Free, transform energies. Log Template. Genealogy Log With! Your body is a component and Raters Achieve, it is not the only one. The shapes inherent in the human body have certain geometric context that is Research Genealogy Log With, revealed in the book and it is about your health, too. You will like and appreciate the simplicity and the power of Elizabeth Senior Marketing Manager numbers. The Pythagorean management of numbers takes you on the road to Sample Evernote Genealogy, reality and invites you to drive it as well. Go or select another topic from the gold post.

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