Pyramid & Pi

Pyramid & Pi
The curious synchronicities of the pyramids

The Pi-Mystery

http://http://doernenburg.alien.de/alternativ/pyramide/pyr00_e.php
http://http://www.crichtonmiller.com/Pyramid%20maths.htm
http://http://www.world-mysteries.com/sar.htm

Long before anyone had expressed the suspicion that Atlanteans or Aliens had built the pyramids, they were believed to be signs from God. Early christian and islamic historians believed, that they were stores, built to survive the Flood.
In the 19'th century some discoveries seemed to strengthen the point, that the building of the monuments was influenced by some higher being. This lead directly to the so called "Pyramid Mathematics" or Numerology. Many people believe, that the mysterious connections found are a sure sign of a greater plan in these monuments. The most famous sign is undoubtedly the mysterious Pi, built into the very fabric of the greatest monument of mankind, the Cheops-pyramid.

What is Pi, and how it can be found in the Pyramid?

Pi in itself is not a mysterious or even magical construct. Pi is simply the value you have to multiply the diameter of a circle with to get its circumference. The rough value of Pi can be obtained through simple experiments. You take a wheel of 1 meter diameter, roll it on the ground for a complete revolution and measure then the distance it has gone on the ground. No secret, it will be something around 3.14 meters. Or you can wrap a rope around a wheel and measure its length. The old Egyptians simply used 3 as a multiplicator, this is precise enough for every-day applications. Much later, hundreds of years after the building of the pyramids, they used 3 + 1/7.

The real secret: Pi is an irrational number with indefinite decimals, and it can be calculated to more than two decimals only, if you have enough theoretical knowledge about geometry - and this the ancient Egyptians never had! It is impossible with any wheel to get more a more precise result for Pi than "3.14 +/- 0.05", so a more precise value found in the dimensions of a building must be the undisputeable proof of some higher involvement.

The pyramid of Cheops hase a base length of 230,38 m, and a height of 146.6 m. If you take two times the base length, and divide this by the height, you get a value of "3,14297...". Not that good, but better than the old Egyptians ever could have estimated. Is this the sign the so called prae-astronauts are looking for?
As you can guess, the scientists are saying "No". But why, do they have a better explanation? Some scientist are arguing, that the value of Pi is pure coincidence. Quite a coincidence, to build Pi to the 4th decimal. By the way, there are several other pyramids with Pi, even with a greater precision! More coincidences?
No, other scientists invented another theory to explain Pi. Unfortunately without much thinking about. They claim, the pyramids contain Pi because of the measurement methods used in the old times. The Egyptians measured distances in "royal cubits" with 52.36 centimeters per cubit. The base of the Cheops-pyramid is exactly 440 cubits long, the height is 280 cubits. But how to measure such great distances? Engineer T.E.Conolly argued, that ropes of this length would tend to break or change length due to the force needed to keep them straight. So this way of measuring distances would be unpracticable for great distances, instead the Egyptians used wheels or drums with a cubit-diameter. To measure length units, they simply rolled the drums over the ground and counted the revolutions. To measure the height, they stapled those drums, nothing secret to be worried about.
Many "rationalists" quickly jumped to this theory, glad to have a simple explanation for this unwanted mystery. The theory was published in many books, and in the the popular German science-show "Querschnitte" the TV-presenter Hoimar von Dithfurt explained to its millions of onlookers, that this was the ultimate solution to the riddle.
Fine. But wrong. Sure, this method can explain the pyramid of Cheops. And the pyramid in Medum. But not much more pyramids. If you calculate the Pi-value for the neighboring pyramid of Chefren, you will get a simple "3" as a result. No Pi in sight. Or its neighbour, the pyramid of Mykerinos. Its Pi-value is 3,26..., no Pi in sight there, too. If they had really used such a method, Pi must be built into every single of the 90 pyramids in Egypt, and not just in two or three of them.

Oh, and let's not forget another problem. The pyramid of Cheops is 440 cubits wide, as can be seen from chiseled lines on the base plateau. But how can you measure 440 cubits by counting revolutions of a drum? You must turn the drum exactly 140,0564 times. You will find similar situations with other pyramids, too. 130.825 revolutions are necessary to measure the length of Chefren's pyramid. To construct the base lengths of all the pyramids, the Egyptians had to know the exact value of Pi to know how many revolutions and fractions of revolutions were necessary. And this they didn't and so they couldn't measure the dimensions of the pyramids found as they are. This theory is rubbish.

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!
You 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.....
The value measured directly from Chufus pyramid is 3,142974, both values match with an error smaller than 0,00015! Pi, on the other hand, has a value of 3,141592..., the error between Chufus pyramid and Pi is ten times greater than the error between the pyramids ratio and the "true" 1:22 ratio. A sure sign, that Pi played no role in the pyramid's construction - but no proof.

Proof would be, if most or all pyramids would fit their 1:2x-ratio better than Chufus pyramid fits Pi. Then it would be clear, that the architects and construction workers had methods to build so precise, that the error to Pi in the great pyramid is worse than it could have been, if Pi was really planned. And, the pyramid of Chefren is even more precise: The 1:21-ratio it is built in, leads to an exact 3,0-pi-value. This pyramid is 215,25 meters wide and 143.50 meters high - the resulting value is exactly 3,0000000! In fact, all reconstructable pyramids of Egypt are within 1/1000 of the theoretical slope angle, most of them much better. Instead of one pyramid built by gods, and 89 pyramids whose angle cannot be explained, we have now 90 well defined pyramid angles.

There are several other pyramids with a built in Pi-ratio, too, for example Huni/Snofrus pyramid in Medum. Therefore, Chufus building is not one isolated, special construction. In fact, from the 14 or so pyramids which can be reconstructed good enough, 6 are built in the 1:22 "Pi"-ratio.

This is the definite proof, that no god, astronaut or Atlantean wizard had any intention of coding Pi into one of the many pyramids erected in Egypt. Pi is simply a result of the measurement methods used in old Egypt! This is the end of the Pi-mystery.