Holy Numbers and Sacred Geometry
There is something odd about numbers. Numbers are very much mentioned in ancient scriptures. In the old testament is a whole book which is called numbers. And there are many many more examples in other religions.
I try to collect here some information about why some numbers appear all over and over again.
I think this is important because the universe is a mathemathical place, and answers may lie within this.
It can be hard, though, with no mathemathical background.
Einstein was also looking for the one "unified theory" which could describe the
whole universe. By doing this, he was actually looking for God. There was a
famous discussion between him (God doesn't throw dice) and a colleguae, Nils
Bohr (God does throw dice) if such a theory could be found. Nowaday the
scientists includes the Heisenberg's uncertainty principle in atomic models,
which means that they still cannot calculate the processes inside an atom, and
therefore build in a "chance factor" in their equations. So God is still not
found. (You can also say that God is EVERYTHING what was EVER found, but that is
another discussion :-)
But wait. There IS a lot to calculate in nature, and maybe you can say we are half-way finding THE ANSWER. Look for example at the fibonacci numbers. These numbers are very much used by nature to determine how leaves grow, for example. Yes, Mother nature is calculating too!
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The thing is that a lot of these numbers are mentioned in ancient books and buildings like the big pyramid. So what did the ancients know? Time to investigate.. |
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Euclid
When you start practising Sacred Geometry, the only things you need are a pencil, paper, a straight ruler and a pair of compasses. The art of it is not to measure out angles, like 72 degrees for a pentagram, but to construct them. For example to construct a 90 degrees angle look at te picture in section 4. A straight ruler and a pair of compasses are often called "Euclidean tools" because of Euclid, a mathemathician who lived in Alexandria about 300 BC. He wrote a set of 13 books called Euclid's Elements.
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When the investigator gets into this kind of stuff, in the beginning you get confused by the may numbers being talked about on the internet. But at a closer look ik turns out that there are only a few important ones: a few "normal' numbers like 1,2,3,4,5,6,7,8,9,10,12,60,360,432, and besides that a few 'irrational' numbers, namely the square root of 2 (√2), the square root of 3 (√3), the square root of 5 (√5) , phi, and pi.
4
The number 4 stands for stability.
5
There is a lot to tell about the number 5. When you think of 5, you can think of a pentagram, or the 5 possible platonic solids. Also, the number 5 is important because of the fact that you have a string with 12 knots and you lay them 3-4-5 like below then it forms an perfect right angle. So it was easy for the ancients to make perfect right angles with a rope divided into 12 sections (which brings us again to 12). It is known they did that. Five is also a fibonacci number. After 360 days, there are 5 more days remaining.
Also the mayans used 5 in their ancient calendar. They calculated the precession cylcle (which is 25.920 years, the mayans called this the Great Great year) and divided it into 5 pieces of 5,125.36 years which was called the Great year.
And, the final punch is that the latest science points out that the universe is finite and bounded by dodecahedrons (that is, a solid made of 12 pentagrams !! Check this.
A dodecahedron.
Learn how to make a pentagram here.
6,60,360
360 is the number of degrees in a circle. Why 360? Why not 100 degrees in a circle, for example?
I have been thinking about this for ages. Now i think there are two
solutions: The first possibillity is that it derived from the sumerian
Soss, (60) which was a base number in that time. Why 60? It is possible
that there was another base number, 6, in combination with a decimal (10)
system. (The Sumerians reckoned in periods of 60 years, equal to one
soss, 600 (60 X 10) years equal to one ner, and 3600 (60 X 60)
years equal to one sar.)
The number 6 Possibly derived from the feature that a radius of a circle is
exacly the side of a hexagon drawn in that circle. Do you have a garden? Do
you happen to have a goat in your garden? When you take the rope of the goat
which grazed the grass, then you find that you can lay it along the circle
exactly 6 times. So this number connects a CIRCLE with a
NUMBER, no wonder this is a holy number!
Also,realize that 1+2+3 = 6 and also 1x2x3 = 6, and 60 is divisable by 1 (60),2 (30),3 (20),4 (15) ,5 (12) and 6 (10), so it is very convienient when you can calculate base 60. Even counting with your hands to 60 is possible, because your fingers make 12 pieces on your hand. On your other hand you have 5 fingers, sou you can count 5 rounds of 12 = 60.
I personally think that this has to be the first number whith triggered people to look further for other correlations between a number and a circle. There are correlations with all the other numbers below 10, but because of this first discovery it must have been the primary reason for the sumerians to incorporate the number 6 in their system. (Or an even earlier civilization, cause domestication of animals was from 12.000 BC (domesticated dogs in kirkuk, iraq), probably even earlier than that)
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A hexagon fits exactly a circle, when one side of the hexagon is exacly the radius of the circle. For the same reason as this the circle is easily divisable in 12 pieces, see my page about 12. |
The second reason could be that 360 is related with 720 (2 x 360) , which is the apparant number of sun-disks which fit in a full circle. On a daily basis, due to the Earth's progress in its orbit, the sun appears to move the equivalence of two of its own diameters (i.e., about 1/360th of a full rotation) eastward through the heavens relative to the fixed stars. I can imagine that there was a shaman who put a stick in front, whith exactly the size of the sundisk. When you should make a circle of those sticks, you use 720 sticks for a year. The second 360 being the nights. Note also that in the number 720 is a connection with the number 5 (360 / 72 = 5). This could be very important when you consider numbers as Holy, the 5 connected with the 6.
you cannot simply count the days in a year, how do you know the years end?
when you dont have a device to measure time, how do you know the days are getting longer again? Until the time came when the ancients could accurately measure the length of a day, they could not know when the shortest day was.
So from the above stated i think that the priests calculated the year by using these sacred numbers. Another possibility is that the year really was 360 days. see my page on calendars for that.
Ok, so we can say that these numbers were actually chosen. But still the question remains why the ancients were so interested in it. Well, why are WE interested in numbers? A soon there is an advanced society in place, there is a need for this knowledge. I already mentioned the calculation of the length of a year, but it could also be used for construction work and more. What about when 10 fruits cost 1 'dollar', and you only want to have 7 fruits ? Nowadays we just ask the japanese. But in that time you had to calculate yourself that 10/7 = 1,4285714285714285714285714285714. Besides, when you think about this numbers it gives you a deep understanding of how nature works. The number game was very much played by alchemists and occultists, and considered very holy in medieval times. (did you notice the calculation above 10/7 gives you a repeating secuence? does that make a priest think about numbers?)
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So it was a holy task to do so. Also it is possible that inside this culture that it was fun to play with numbers and try to calculate nature, maybe for the glory of God. Nowadays many people look at sacred geometry and gematria. And when a lot of people join into this, there is a lot of combined brain-power. Also keep in mind that between the official figures of the first human at 100.000 BC (some say even 200.000 BC), and the sumerians 3500 BC, the ancients had 96.500 years to figure this out. Realize that people could count long before they could write. The earliest known example of writing are some clay tokens from a site called Choga Mish in Iran. It is from around 8000 bc. The tokens were probably used to depict amounts of goods like grain. So it means they were counting the goods. Writing is considered to have begun with the sumerian pictographic script, about 3400 BC. |
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So it is very well possible that the ancients knew about the square root of 2, pi(3.14), Phi(1.618), phi(0.618), etc.. So why did the ancients use this holy numbers into their buildings? People like to think (including me, to be honest) that is is a message to us. But it is also possible that the ancients thought is was the strongest way of building (maybe they were right ;-), or maybe it was concidered Holy to use these numbers.
7
Did you know that the number 7 is the only number what does not fit in a circle? i mean, when you try to construct a heptagon (7-sided) in a circle, you cannot make it precicely. The angle to use is not a regular number like when you divide a circle into 2,3,4,5,6,8,9 or 10 pieces, but it is an infinite number (51,428571428571428571428571428571 degrees, note the sequence in this number).
8
In China 8 is considered a lucky number. I made a special page about dividing a circle in 8 pieces, which turns out to be not so easy (with only euclidian tools)
12
12 is the number hours in a day, the number of zodiac-signs, the number of aposteles, and the number of balls that fit around one ball of the same size. 12 has also a connection with 6 (2x6=12) and 60 (5x12=60, 12 connected with 5, very important). I prove in my page about construction of 12 that it is easier, and much more precise, to divide the universe in 12 pieces instead of 8.
I wandered for ages about why geographical maps have 8 cardinal points (North, NE, East, SE, South, SW, West, NW) instead of 12. But when I studied a book about maps i realized that the older maps ARE divided in 12 pieces ! An example below is from Lienhart Holle in 1482 AD. This is an edition from the geographical text of Claudius Ptolemy (or Ptolemaeus), a Greek astronomer and geographer working in Alexandria, circa 150 A.D. Note the 12 'wind-blowers'. The ealiest map divided in 8 I found came from 1564, so somewhere in the past 80 years this view about cardinal points changed.
The reason why the world changed to an 8-fold pattern is not clear to me. It could be that there is an occult reaon for it, the heavens divided in 12 and the earth in 8; this being the number of stability for ages.
Phi (± 1.6180339887...)
Phi is a number which has no exact value (approximate value = 1.61803...). The unique properties of Phi are that phi +1 = phi squared and also 1 + 1/phi = phi. The Phi ratio is the basis for the Fibonacci sequence 1,1,2,3,5,8,13.,21,34... which was not generally publicized until 1200 A.D.
phi ± 0.6180339887... (spelled with lower case p) is a relative to Phi
for an exellent site about this subject, see this site.
Phi is is a very importent number for Mother Nature, because a lot of stuff in nature is related to this number. By artists this number is called the "golden number" or the "golden ratio" because they used it in their paintings. The Phi ratio is also the base for the fibonacci sequence. This fibonacci sequence is a general rule for plants and animals how to grow.
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as you can see, phi can be drawn with only a straight edge and a pair of compasses this way. see at 4 how to make a square without using a 90 degree edge. |
Square Root of 2 (√2) (1.4142..)
De square root of 2 is estimated by the egyptians as 256/181, that is only .00015 less than the true value = 1.4142
Square Root of 3 (√3) (1.732..)
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De square root of 3 is the hight of a vesica piscis (latin:fish bladder) when the length is 1. A visica piscis is the shape which formes when you draw two circles with the centers on each other. It looks a bit like a fish. One courious thing about it is that it was mentioned in the bible by the 153 fishes Jezus caught with his disciples, the shape of a vesica piscis being 153:265, this is known as the 'measure of the fish'. It is a powerful mathematical tool, being the nearest whole number approximation of the square root of three. This shape you will see in many designs of cathedrals. Did you ever realize that when you walk in a cathedral, you enter a giant womb to get back to your source and get reborn again when you exit? I think this view didnt survive the middle ages :-)
Simon Peter went up, and drew the net to land full of great fishes, an hundred and fifty and three: and for all there were so many, yet was not the net broken. jhn 21:11 bluletterbible In countries like the USA there are bumper-stickers of a fish, to show you are a christian. It is considered christian when the fish swims to the left, and the devil when it swims to the right. This is a good example what is left of of Holy Knowledge after the medieval times. |
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Square Root of 5 (√5) (2.236..)
De square root of 5 is equal to Phi + phi.
phi (with small letter) is the other side of Phi, namely 0,618..
| According to my windows calculator: | 1.618033988749894 + 0.618033988749894 = | 2,236067977499788.. |
| √5 = | 2,236067977499789.. |
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Inside a vesica piscis construction the √2, √3, and √5 are found:
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pi (p)
The number pi is the number of times the radius of a circle fits into the circumference. it is about equal to 3.14
This site is called "the friends of pi"
The first known account for pi is about 1650 BC in the Egyptian Rhind Papyrus. p = 4(8/9)2 = 3.16
153
There is something odd about the number 153. It was already mentioned on this page as being the closest approximation to √3 as 153:265. On this page you will find another odd calculation: if you take numbers dividable by 3, like 3, 6, 9, 12, 15, 18, 21, 24, 27...etcetera, you will find when you cube (n * n * n) each digit and add the results, and if nessecary repeat that, you finally gain 153 in all cases. Lets take for example the number 27:
(2x2x2) + (7x7x7) = 8 + 343 = 351 (now take that answer (351) and do the calculation again)
(3x3x3) + (5x5x5) + (1x1x1) = 27 + 125 + 1 = 153
This is always true, on this page I demonstrate that for the first 50 numbers
Another odd thing about 153 is this:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 = 153
and related to that:
Prime numbers through number 17 would be: 1, 3, 5, 7, 11, 13,17. (a prime is a number what you only can divide to itself and 1). 17 is the SEVENTH prime number.
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The vesica piscis as a function of 153. |
432
The number 432 is also an important one. There are people who like to see that the A tone on a musical keyboard is re-defined as 432 instead of 440 Hz. (Hz is the number of cycles per second). See here
By the way, there are 43,200 seconds in our time measurement of 12 hours.
Als, 60 x 432 is 25.920, the presumed periods of years for 1 < HREF="moveEarth.htm">precession cycle