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Author Topic: Sacred Geometry
Telperion the Silver
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Greetings all!
I thought I'd open a thread on the fascinating topic of sacred geometry. The Greeks, among others, believed that numbers and perfect shapes could explain the nature of the Universe. And in fact, amazingly enough, they can! The structure of matter, life, and energy form themselves around them like flowers, starfish, or snowflakes. I'll start by talking about two…the two most obvious, and my personal favorites.

Whatever direction you have it, the Pentagram is one the greatest pieces of sacred geometry and probably the oldest. Countless flowers and other life forms base themselves around the five pointed star. It represents the five elements coming together as well as the Sacred Feminine.

The greatest is probably the Full Tetractis...created by Pythagoras as the symbol of the Cosmos... later adopted by the Hebrews as their sign for God. The Greeks saw the number one as sacred as the point of beginning and 10 as sacred as the point where the cycle repeats. One is for Unity, Two is for Conflict, Three is for Resolution, etc..etc… Three was very sacred as the first geometric shape, the Eternal Triangle. Pythagoras and his buddies noticed that when you added 1 + 2 + 3 + 4 you = 10! *gasp* They equal to an already sacred number! So that sequence must be important. Pythagoras represented that sequence as a pyramid of dots. The Tetractis. Eventually he went on to stabilize the structure by adding three more points created the Full Tetractis, aka the Star of David by the Hebrews centuries later. More specifically the 13th point in the center of the Full Tetractis is the symbol of the Cosmos/God. Thus 13 is the most sacred number in the Universe! (Isn't that awesome!) When the early Christians were trying to convince the Empire that they really weren't Jews, they cast away many of the old associations the Jews had and called them evil; even when those associations happened to be mathematically true and sacred to the world, not just Jews.

What other cool facts do people know about sacred geometry or numbers? [Smile]

[ September 17, 2004, 01:35 PM: Message edited by: Telperion the Silver ]

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Annie
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I just bought a cool-looking book on the Golden Ratio and sent it to my Mom without reading it. She's writing a paper and needed it more than me.

It was probably really great, though. [Smile]

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pooka
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:cough cough:
I guess imitation is the highest form of praise.
[Wave] [Hail] telp

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Telperion the Silver
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*winks at Pooka*
[Smile]

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Farmgirl
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Hmmmmm

Telpy,
With all that you see in the structure of what you have discovered in sacred geometry -- you still believe that all those intricacies evolved from chaos and a primordial pool of random stuff, instead of seeing it as just a possibility of some type of intelligent design?

Farmgirl

(no, I'm not trying to hijack this thread -- I'm trying to see how Telp can believe two different things and think they mesh)

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sarcasticmuppet
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In my MESA class we had a segment on Islamic art, and how it involved extensive geometric designs. There was one really complicated one that almost had the look of a celtic knot, and we discussed how it represented the Muslim idea of Infinity.

A quick Googling brought me
this:
quote:
Both the contemplation of and the creative skill in making patterns lead in their own way to an understanding of the perfections of Universal Nature as it moves the elements. Islamic pattern, unique as an art form, is also unitary in its aim and function. Symbols can exhaust verbal explanation but verbal explanation can in no way exhaust symbols -and the symbols inherent in Islamic pattern and geometry are directed towards that undifferentiated unity.

Thus, the circle, and its centre, are the point at which all Islamic patterns begin and is an apt symbol of a religion that emphasizes one God, symbolising also, the role of Mecca, the center of Islam, toward which all Moslems face in prayer. The circle has always been regarded as a symbol of eternity, without being and without end, and is not only the perfect expression of justice-equality in all directions in a finite domain--but also the most beautiful parent of all polygons, both containing and underlying them.

From the circle comes three fundamental figures in Islamic art, the triangle, square and hexagon. The triangle by tradition is symbolic of human consciousness and the principle of harmony. The square, the symbol of physical experience and the physical world-or materiality-and the hexagon, of Heaven. Another symbol prevalent in Islamic art is the star and has been the chosen motif for many Islamic decorations. In Islamic iconography the star is a regular geometric shape that symbolizes equal radiation in all directions from a central point. All regular stars -- whether they have 6, 8, 10, 12, or 16 points -- are created by a division of a circle into equal parts. The center of the star is center of the circle from which it came, and its points touch the circumference of the circle. The rays of a star reach out in all directions, making the star a fitting symbol for the spread of Islam.



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kaioshin00
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quote:
1 + 2 + 3 + 4 you = 10!
I thought 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

[ September 17, 2004, 01:58 PM: Message edited by: kaioshin00 ]

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Telperion the Silver
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No probs Farmgirl! [Smile]

Ok... So Chaos as in void or as in random/disordered? Because in perfect Void it is possible for ANYTHING to happen.

As for random/disordered... it only SEEMS random to us Humans. The randomness of a cloud or how a tree grows is actually not random at all: Fractals. You look at a jagged rock and it seems random...but get close enough and you see a perfect grid of atoms.

There is inherent structure to the Universe and all the forces in it that has nothing to do with intelligence. The Universe is one huge mathmatical equation working itself out. The only place where it changes is where sentient creatures come into play... us. [Smile]

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pooka
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I thought the Islamic focus on geometry came in part from an extreme interpretation of the commandment not to have idols. So they couldn't depict people or animals in art, and it comes out instead in elaborate designs. In a way, one could cry "censorship" but the art is still there, it just goes into unique and interesting forms.

P. S. I don't know if this resulted directly in the Arabs preserving the geometry and mathematical theory of the Greeks, but it may be that Islamic repression is directly responsible for us having the technology that we do today.

[ September 17, 2004, 02:04 PM: Message edited by: pooka ]

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Raia
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Alright, that's it... WHAT is up with all the math threads lately?!
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Telperion the Silver
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Must be in the air...

*cough*cough*

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Farmgirl
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quote:
There is inherent structure to the Universe and all the forces in it that has nothing to do with intelligence. The Universe is one huge mathmatical equation working itself out
Okay.... I'm still having a hard time wrapping my mind around this --- you mean the "mathmatical equations" could come from nowhere -- from no intelligence (alien or otherwise)? That the perfect order could come from nothing? Structure can come without intelligence?

If you put all the pieces of a pocket watch into a shoebox and shook it up for years and years, would it eventually fall into place all put together as a perfect watch?

Farmgirl

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beverly
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When I was a kid, we had a taped-off-TV recording of "Donald Duck in Mathmagic Land". It was really corny and cheesy, but I loved it! It was where I first learned about the golden ratio and have been fascinated ever since. [Smile]

The show ended with the quote:

"Mathematics is the language with which God wrote the universe."

~Galileo Galilei

[ September 17, 2004, 02:14 PM: Message edited by: beverly ]

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TMedina
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Or it happens that math follows a parallel logical model which mirrors the Universe.

The only mystical, magical numbers I'm worried about at the moment involve my checking account.

-Trevor

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Telperion the Silver
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quote:
Okay.... I'm still having a hard time wrapping my mind around this --- you mean the "mathmatical equations" could come from nowhere -- from no intelligence (alien or otherwise)? That the perfect order could come from nothing? Structure can come without intelligence?

If you put all the pieces of a pocket watch into a shoebox and shook it up for years and years, would it eventually fall into place all put together as a perfect watch?

No... because the watch is a Human made thing. (well, given an infinite amount of time they would) They would fall into an order that made sense for what they are, what they are made of, how heavey they are, etc... Even that "random" falling is actualy order and pattern.

The question on "where did it ALL come from" is different. We can never know what happened before the Big Bang. (Unless we evolve to pan-dimensional beings or something.) The "mathematical equation" of the universe started with the creation of energy and matter. What we call Laws of Nature are just our observations on how matter and energy interact. After the Universe was formed these laws set the boundaries of the "equation" of the Universe and how it would grow and change and maybe die.

But now intelligent life evolves...by our actions we change the equation a little bit. If we live long enough and become powerful enough we can change the fate of the Universe.

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Telperion the Silver
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quote:
Or it happens that math follows a parallel logical model which mirrors the Universe.
THAT'S IT!! [Smile]
Summed up in one sentence... rock on!

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Stray
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quote:
The only place where it changes is where sentient creatures come into play... us.
Why do you say that?
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MrSquicky
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Telp,
The pentagram is even cooler than that. From what I remember, the transits of Venus over a certain period of time (I think it's 8 years) actually form an almost perfect pentagram, but with the end point slightly off from the start point. However, over the course of 360 years, it ends up back at the same point. This 360 number is the reason why we regard a circle (or cycle) as having as many degrees. It also was used by some ancient civilizations (I'm pretty sure the Babylonians were amoung them) as the foundation of their calendar of 60 (magic number and the numbers of seconds in a mintute/minutes in an hour) weeks of 6 days each with one week of 5 days that were considered both holy and not part of any year.

Here's a link to some venus pentagram information. The rest of it, I picked up in various comparative mythology sources and shouldn't be all that hard to find.

Another cool bit of "sacred" geometry that has to do with circles and quite possibly astronomy is the mandalic picutre of of the Daoist yin-yang symbol. Here's a link about the possible astronomic significance of it. As for the circle thing, draw two circles of equal size one on top of the other, with the highest point of the bottom one just touching the lowest point of the top one so that the tanget of this intersection point is a perfectly horizontal line. Ok, now draw a circle around these two circles with the containing circle touching the highest point of the top one and the lowest point of the bottom one, also so that the tangets are horizontal. Now erase the left half of the top circle and the right half of the bottom circle and you've got the yin-yang mandala.

Each mandala contains two other mandalas with the total circumfrence of the sub-mandalas being equal to that of the parent mandala and the total area of the sub-mandalas 1/2 that of the parent. This process can be repeated infinitely.

Each yin or yang can be broken down into another yin-yang system, such that you can talk about the yin of the yin and the yang of the yin.

I always thought that that was pretty cool.

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cyruseh
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I tried to figure it out, but how did you get 13 from the star of david? I couldnt find all the points.
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Telperion the Silver
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Why? Since we are self aware, we can change the outcome of the "equation" by our actions. Outcomes that would not have happened without our activities. Of course, currently we can only effect Earth: burning trees and fuel, war, building cities, etc...

But if we advance to the stars and survive for a LONG time we change much more. Butterfly effect.

[ September 17, 2004, 02:41 PM: Message edited by: Telperion the Silver ]

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miles_per_hour
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quote:
We can never know what happened before the Big Bang. (Unless we evolve to pan-dimensional beings or something.)
Actually, that's really close to what I believe can happen to us in the next life.
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Hobbes
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Farmgirl, here's an attempt at a secular explenation. Where the laws come from that formed the universe is unknowable from science's standpoint, at least right now and into the foreseeable future. But if we start with the knolwedge that their are laws that govern the universe, then we can see that patterns emerge. Mathematical equations "tend" to specific patterns. I wish I had more time and I could draw up some diagrams, ... I guess I'll just do the best I can with my poor words. [Smile]

Let's start simple. Take the equation y = 1/x. You can see that as the equation progresses along x you will get answers closer and closer to 0. Thus the equation is said to "tend towards 0". Meaning that despite the fact that you could enter in any number you can think of, including negatives, you'll get a number close to 0 a lot. Or, depending on how you want to inturpret the meaning of the equation, no matter where you start on it, you'll wind up heading towards 0.

Well when you start taking more complex, non-linear equations (of special interest is non-linear differential equations, but it's not really important what those are if you don't already know) you'll find that they don't necessarily tend to one particular number, as to specific patterns. No matter what data you start with, or data within a certain range, you'll wind up with simlar patterns. These patterns are called "attractors", because they "attract" the equation. In perhaps the most famous one, a "strange attractor" (not important what the addition of "strange means", just some vocab [Smile] ) you'll see a kind of figure 8. It doesn't matter what numbers you put into this equation, if you plot it out you'll wind up with soemthing similar to a figure 8. And yet the chaos still emerges, because predicting where you'll be in that figure 8, or how far off from a "perfect" figure 8 (and this thing is in 3D) is simply impossible to predict without knowing in detail all the intial data your plugging into the equation.

So the idea here, is that with random intial conditions but specific rules, you can have chaos (the unknown deviance from the ideal attractor) and yet the universe will "tend" to a specific attractor, whatever attractor matches the equations that govern the universe.

Hobbes [Smile]

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Telperion the Silver
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quote:
I tried to figure it out, but how did you get 13 from the star of david? I couldnt find all the points.
I'll show you! [Smile]

.
. .
. . .
. . . .

That's the Tetractis.

Pythagoras created the Full Tetractis:

.
. . . .
. . .
. . . .
.

There we go! The central 13th point is the symbol for the Cosmos.

[Damn! Didn't work... let me try that again]

[ September 17, 2004, 02:45 PM: Message edited by: Telperion the Silver ]

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cyruseh
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I think i got it, there is a point in the middle of the star?
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Stray
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quote:
Why? Since we are self aware, we can change the outcome of the "equation" by our actions. Outcomes that would not have happened without our activities. Of course, currently we can only effect Earth: burning trees and fuel, war, building cities, etc...

But if we advance to the stars and survive for a LONG time we change much more. Butterfly effect.

Sorry, I still don't getcha. What does being sentient/intelligent have to do with it? I don't see how that makes us very much different from any other lifeform or phenomenon in the universe, at least not in the Grand Scheme Of Things. Sure, we can come to understand at least some of the laws that govern the universe, but that doesn't mean we can change them, or that we're not controlled by them the same as anything else.

Gah...this is well on the way to thread derailment. Feel free to discontinue if you wish.

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the master
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quote:
if we start with the knolwedge that their are laws that govern the universe, then we can see that patterns emerge
you spelled it wrong. it's spelled a s s u m t i o n.
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Hobbes
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*cough* I meant if someone handed us down a big hunk of knolwedge that included this information... yah, I meant assumption. [Embarrassed]

Hobbes [Smile]

[ September 17, 2004, 02:59 PM: Message edited by: Hobbes ]

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Annie
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but not assumption, because that's spelled a different way [Razz]
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the master
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i was sort of hoping hobbes would catch that. you know, eye for an eye. but it looks like he took my spelling, saw your post and then fixed his.

[ROFL]

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Hobbes
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Actually, I posted the correct spelling, then saw yours and changed it, because when have I ever been right about spelling? Then [I] saw Annie's and changed it back. Even better! [Laugh]

Hobbes [Smile]

[ September 17, 2004, 03:05 PM: Message edited by: Hobbes ]

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TomDavidson
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Another important thing to keep in mind about ANY kind of numerology is that a number is only "important" because someone says it is. So if one number is added together to another number to make a third important number, that EITHER means that these important numbers are related in some way, this has been a coincidence, OR -- as is more likely, in most cases -- the numbers have been assigned importance precisely due to properties that wind up relating them to each other.
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Telperion the Silver
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For me that's why I find sacred shapes so interesting, because they accidentally reflect the structure of the universe. [Smile]
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beverly
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Alma 30: 44

44 ...yea, and all things denote there is a God; yea, even the earth, and all things that are upon the face of it, yea, and its motion, yea, and also all the planets which move in their regular form do witness that there is a Supreme Creator.

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Stray
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I've always been a fan of the number e and the logarithmic spiral, personally. Mainly because that exact spiral shows up all over the place in nature, in seashells and sunflowers and so on, and because the formula for deriving e ( (1/0)! + (1/1)! + (1/2)! + (1/3)! + (1/4)!...) is aesthetically pleasing. If I believed in a god, this would be like discovering secret messages from him/her/it. As it is, it's just really freaking cool.
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Maccabeus
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Romans 1:20

For since the creation of the world God's invisible qualities--his eternal power and divine nature--have been clearly seen, being understood from what has been made, so that men are without excuse.

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MrSquicky
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If we concede that everything there is gives conclusive proof that the Christian God exists and that the only people who deny this do so because they are so incredibly evil and selfish, would that let us get back to the actual interesting topic of this thread?

Or do I have to get back into my "Yay Jesus!" cheerleading outfit again?

[ September 17, 2004, 03:56 PM: Message edited by: MrSquicky ]

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Stray
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Meee-YOW! [Wink] *gives MrSquicky a catnip-encrusted tuna filet*

Ooh, and edited for double the cattiness! Yay!

...I'm not trying to be sarcastic, sir, I actually really enjoy your sense of humor [Smile]

[ September 17, 2004, 04:03 PM: Message edited by: Stray ]

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Farmgirl
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touche' Mr. Squicky...

...but you will notice I was very careful to never use the word God when I originally went that direction -- I only wanted throw out the possibility of intelligent design -- whereever that might come from (after all, some believe we all came from aliens).

And I promise to post no more along that line in this thread...

FG

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beverly
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Might I point out that neither scripture makes mention of Christ? Both only express the idea that the order of the universe around us is a testament to a Creator.
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TMedina
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Well, to be fair, we are talking about sacred numbers and finding higher meaning in mathematics and similar fields.

All things Divine would probably have manifested sooner or later.

-Trevor

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Dan_raven
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The Magic Square is a 3000 year old Chinese divine arrangements of numbers.

4 9 2
3 5 7
8 1 6

This arrangement of numbers has a wide range of special properties.

They are the prime numbers between 0 and 10.

Add each collumn and you get 15
Add each row and you get 15
Add each diagonal and you get 15

Internet problems now. I'll add more to this later. Google Magic Squares

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Stray
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quote:
They are the prime numbers between 0 and 10.
Psst...not prime numbers, integers.
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Dan_raven
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Sorry, Integers. I was fighting internet problems and confused my terms.

However, according to legend, a city was threatened by a flood. The people gathered up a stuff to sacrafice to the river god. Nobody knew how much to give, so they piled there offerings on the bank.

Three times they did this, and a large turtle came out of the water and crept around the sacafice, but it was not enough.

On the third time, a little girl noticed the markings on the turtle's back. It was this magic square, with the Odd numbers being the Yin and the Even numbers being the Yang. This told them how to sacafice, and save their village.

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Dagonee
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All anyone needs to know about sacred geometry and numbers.
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Farmgirl
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wow -- that site is hard on the eyes!

FG

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Dagonee
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Hard on the brain, too.
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katharina
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quote:
Humans exist as CUBICS, not entities,
for the 4 corner stages of rotating human
metamorphosis do not occur at the same time
for the individual - except for family Cube.

I love him.
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Dagonee
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I think I could win the $10,000 bet for disproving his theory if I could just figure out what the hell his theory is.

Dagonee

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Hobbes
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Why do you think no one has won it?

Hobbes [Smile]

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