Pyramids and PI

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Pigeon
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Pyramids and PI

Post by Pigeon » Wed Mar 20, 2013 8:16 pm

It was John Taylor who first proposed the idea that the number PI might have been intentionally incorporated into the design of the Great Pyramid of Khufu at Giza.

He discovered that if one divides the perimeter of the Pyramid by its height, one obtains a close approximation to 2PI.

He compared this to the fact that if one divides the circumference of a circle by its radius, one obtains 2PI. He suggested that perhaps the Great Pyramid was intended to be a representation of the spherical Earth, the height corresponding to the radius joining the center of the Earth to the North Pole and the perimeter corresponding to the Earth's circumference at the Equator.

It is true that if one divides the Great Pyramid's perimeter by its height, one indeed obtains a very good approximation to 2PI. An equivalent statement is that the slope of each face of the Great Pyramid is very close to 4/PI=1.273239.... This relationship is accurate to within .04% or better (depending on the data that one uses). That level of accuracy seems very impressive and is certainly the reason that Taylor's idea has been widely promoted and believed. Could such an accurate and elegant relationship be just a mere coincidence?

The main point that I will make in this essay is that when one takes into account what we know about ancient Egyptian mathematics (based primarily on the Rhind Papyrus), especially their ways of representing lengths and slopes, then the relationship between PI and the Great Pyramid no longer seems very remarkable.

The essential point is that the measurement system which the ancient Egyptians used would lead the architects to use certain slopes in the design of pyramids. One of those slopes just happens to be an excellent approximation to the number 4/PI, and if the architect chooses that slope, then the pyramid would exhibit the famous PI relationship. From this point of view, the probability that the architect might choose that particular slope for at least one of the pyramids is actually rather high. It then becomes quite reasonable to believe that the relationship between PI and the Great Pyramid is just an accidental consequence of their Mathematics.

For the GREAT PYRAMID OF KHUFU at Giza, the angle of slant for each face is 51o50'40"
and the inverse-slope of each face then turns out to be .785667. This is quite close to 22/28 = .785714

they used a system of measuring lengths in terms of "cubits," "palms," and "fingers." A cubit is equal to seven palms and a palm is equal to four fingers. Thus one cubit is equal to 28 fingers, and that is where denominators dividing 28 would come from.

Read the complete writeup Here for the background.

The earliest attested standard measure is from the Old Kingdom pyramids of Egypt and was called the royal cubit (mahe).

The royal cubit was 523 to 529 mm (20.6 to 20.8 in) in length, and was subdivided into 7 palms of 4 digits each, for a 28-part measure in total.

Evidence for the royal cubit unit is known from Old Kingdom architecture, from at least as early as the construction of the Step Pyramid of Djoser from around 2,700 B.C.

Wiki

So might PI have arisen from the slope used in the pyramids and the units of measure.

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Pigeon
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Re: Pyramids and PI

Post by Pigeon » Wed Mar 20, 2013 8:33 pm

The Great Pyramid of Khufu
Khufu Belongs to the Horizon

Original Height: 146.6 m (480.96 ft)
Current Height: 138.75 m (455.21 ft)
Length of Side: 230.37 (755.8 ft)
Angle: 51º 50’ 40”
Estimated Volume: 2,521,000 cu m

Image

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Royal
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Re: Pyramids and PI

Post by Royal » Wed Mar 20, 2013 11:19 pm

Stephen Mehler’s fascination with ancient Egypt, which began at the age of eight, has guided his education and spiritual work all his life. Mehler holds three degrees in the sciences and is a trained field archaeologist and prehistorian. Mehler also served as a Staff research scientist for the Rosicrucian Order, AMORC, in San Jose, California from 1978-1980.

For almost 16 years, 1992-2008 , Mehler was a student, disciple, and close friend of Egyptian-born Egyptologist and indigenous wisdom keeper, Abd’El Hakim Awyan (1926-2008), popularly known as Hakim. Stephen has written two books, The Land of Osiris (Adventures Unlimited Press, 2001) and From Light Into Darkness: The Evolution Of Religion In Ancient Egypt (Adventures Unlimited Press, 2005), based on his work and collaboration with Hakim and Stephen’s over 40 years of research in the area. Stephen is currently Director of Research of his own Land Of Osiris Research Project. He also leads tours to Egypt and is working on a third book based on his work with Hakim.

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Royal
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Re: Pyramids and PI

Post by Royal » Wed Mar 20, 2013 11:43 pm

Per - Neter

Pyramidos

Pyramid



Fire in the center

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Pigeon
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Re: Pyramids and PI

Post by Pigeon » Thu Mar 21, 2013 12:50 am

I believe the measurement system led to the PI reference. Although the reference to the Earth might make sense.

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Re: Pyramids and PI

Post by Pigeon » Thu Mar 21, 2013 2:48 am


But there is, in fact, a really simple explanation for the Pi-mystery. It has something to do with the way the Egyptians measured angles. Our concept, to measure the tilt between lines and to call them "angle" is and was not known to all cultures. The Egyptians used another way: They measured the horizontal distance of a slope, necessary to cover the height of one cubit. This distance was measured in palms or fingers, 28 of them fitted into one cubit.

The Egyptian number system was different, too. They used a simple decimal system, but in another way as we know it. We have 10 different ciphers from 0 to 9, and the position of such a cipher in a number defines its value, eg. "12" has definitively another value than "21", although both numbers use the same ciphers. The Egyptians used different symbols for multiples of 10: A dash for a single number, a hose shoe for 10, a tape measure for 100 and so forth. The figure "12" was expressed by two dashes and one horseshoe, "21" as two horseshoes and one dash. The position of the horseshoes and dashes in the writing was absolutely irrelevant! Such non-position bound number representations have no concept for zero, and normally no concept of fractions, too. An Egyptian could not have used values like "2.537 fingers". The only fraction types later Egypt knew was "one divided by something", marked with an oval on top of the number.

Egyptian engineers only used whole fingers for the construction of their buildings. Because of this, the number of useable "normal" pyramid angles was limited to 28, between 1 Finger to 1 cubit (nearly 90 deg.) and 28 fingers to 1 cubit (45 deg.). And, in fact, all pyramids found in Egypt are built in such a whole-finger-ratio!

Pyramid anglesYou can see some of the possible pyramid angles here. The 1:22 ratio as found in the pyramid of Cheops is the most pleasing one for the human eye. Ratios under 1:20 were impossible on monumental buildings, as the half finished buildings in Meidum, Dahschur (bent pyramid) and Abu Roasch suggest, ratios higher than 1:24 are looking a little lame. Only two Pyramids are not built within the "One cubit to max. 28 finger"-range: The top of the bent pyramid, and the red pyramid. But both are built in a whole finger/cubit ratio too: 1:31. Some other examples: Pyramid of Chefren: 1:21, Pyramid of Mykerinos: 1:23, Pyramid of Djedefre: 1:23, Step pyramid of Djoser: 1:25.

But what about Pi? As you remember, the Pi-value was calculated from "two times the base length, divided by the height". The 1:22-ratio describes the height to the half base length, so 88:28 (four times the half base, divided by height in fingers) describes the value encoded into a true 1:22-slope. The result is 3,14285714.....

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