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Ambient I
Plečnik: "Angle" of Judgement
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Great Pyramid-King Chamber |
by David Bowman
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The best place to search for the original Egyptian measure is the place suggested by Petrie, the King's Chamber inside the pyramid. It is impossible to find a module of the dimension if the dimension are too big, there are many possible solutions. But in a small place, where the dimensions are much smaller, in the core of masonry where the stability is best, the workers must have done the best job, most precise since it should be the sacred place of the pyramid.
The floor plan proves to be the key, because the sides of the floor plan are exactly in ratio 2 to 1, or two squares. Measurements available prove that it is almost a perfect ratio 2:1, 412.5' (1048 cm) in width and 206' (524 cm) in breadth. This proportion 2:1 mentions Plato while describing the temple of Poseidon in the center of Atlantis, and it is also a proportion of Hikal, the great hall of Solomon's Temple and its predecessor Tabernacle, before the cubical Holy of Holies. Dimensions of the hall in Solomon's Temple, 20 cubits in breadth and 40 long, are described in Bible, and prove that the basic dimensions are always rational small numbers, in this case 40:20 = 4:2 = 2:1. Many Greek temples' plans are also in proportion of the double square, and it seems that this ratio was used for the prestigious religious compositions. In Scotland there is one Rosslyn Chapel which has for the floor of the sanctuary also two squares.
Sir Flinders Petrie deduces the measure employed from the dimensions of the floor plan, approximately a measure of 20.632' (52.4 cm):
Probably the base of the chamber was the part most carefully adjusted and set out; and hence the original value of the cubit used can be most accurately recovered from that part. The four sides there yield a mean value of 20.632 ? .004, and this is certainly the best determination of the cubit that we can hope for from the Great Pyramid.
This measure is the meh, royal Egyptian cubit measured and researched by many researchers, and it is subdivided into 7 palms or 28 digits. Considering the dimension of royal cubit, the width of the King's Chamber, 412.5' (1048 cm) equals 10 royal cubits, and the length, 206' (524 cm), 20 royal cubits. The height of the King's Chamber is not so straight forward as the previously described measures, since the royal cubit doesn't seem to fit precisely in 229.6' (583 cm). There are a few possibilities concerning the reasoning about the height of the King's Chamber:
- it is geometrically related to other dimensions, hence irrational value;
- it is a fraction of a royal cubit, not a whole number;
- the height is proportioned in another 'base' measure than royal cubit;
- the height was not carefully built or tectonic movements changed it.
Since the first proposition contradicts the described method of investigation it will be abandoned, for many solutions are possible but no trace of canon in such attempts, since other measures prove different, they are interconnected through modules or its subdivisions. The last proposition could be in fact only a safety valve if every other line of research proved futile. The important information is that the royal cubit equals to 7 palms or 28 digits, whereas another Egyptian cubit known, a 'common' cubit, which equals to 6 palms or 24 digits:
20.632 x 6/7 = 17.685 (44.92 cm) = common cubit
This 'common' cubit, which is 6/7 of the royal cubit, seems to fit almost perfectly thirteen times in the height of the King's Chamber:
13 x 17.685 = 229.9 (583.95 cm) which is very close to the mean height of the King's Chamber 229.6 (583.18 cm)
If the above guessing is correct, then the dimensions of the King's Chamber, expressed in digits as a common denominator, would be:
| dimension |
b. inch |
cm |
royal cub. |
cubit |
palm |
digit |
| width |
412.5 |
1,048 |
20 |
|
140 |
560 |
| length |
206 |
524 |
10 |
|
70 |
280 |
| height |
229.6 |
583 |
|
13 |
78 |
312 |
| sum |
|
|
|
|
288 |
1152 |
Such a cubus has also a certain peculiarity, that its space diagonal equals almost exactly 700 digits: sqr(560*2 + 280*2 + 312*2) = 699.53.
The biggest common denominator of all main mean dimensions is a measure called dichas or two palms equal to 8 digits:
560 = 70 x 8 = 70 dichas
280 = 35 x 8 = 35 dichas
312 = 39 x 8 = 39 dichas
The sum of all three extremities 70 + 35 + 39 is 144, the number that is highly appreciated by St. John for the description of Heavenly Jerusalem and other data in the Apocalypse:
KJV Rev 21:16 And the city lieth foursquare, and the length is as large as the breadth: and he measured the city with the reed, twelve thousand furlongs. The length and the breadth and the height of it are equal.
KJV Rev 21:17 And he measured the wall thereof, an hundred [and] forty [and] four cubits, [according to] the measure of a man, that is, of the angel.
According to Apocalypse the city of Heavenly Jerusalem was cubical, measuring twelve thousand furlongs or 144,000 cubits in all directions. Note that also the King's Chamber is composed out of a square, at least the floor plan represent two squares, or ratio 2:1. The other quotations from the Revelation are suggestive while keeping in mind the context of the King's Chamber:
KJV Rev 7:4 And I heard the number of them which were sealed: [and there were] sealed an hundred [and] forty [and] four thousand of all the tribes of the children of Israel.
KJV Rev 14:3 And they sung as it were a new song before the throne, and before the four beasts, and the elders: and no man could learn that song but the hundred [and] forty [and] four thousand, which were redeemed from the earth.
The other possibility concerning the mean height of the King's Chamber is to follow the prescription successful at other two mean dimensions, width and length. Petrie produced the royal cubit by dividing the width by a tenth. Width and height are related to each other in ratio 1:1.1126 which is approximately 10:9. Therefore a new measure is obtained by dividing the height in ten parts, just like Petrie did with the floor plan:
583 cm = 10 x 58.3 cm = a new measure
This new measure is related to the royal cubit through ratio 9:10 just like the ratio of width to height:
52.4 x 10/9 = 58.22 cm which is close to 58.3 cm.
But this measure was not found in other places of the Great Pyramid, so it is highly unlikely that this is the right solution.
Value of Pi in King's Chamber
Two squares for the ground plan also conceal a geometrical peculiarity, for it contains a very accurate approximation of Pi. The sum of two sides of the rectangle together with the diagonal represent a fraction of Pi. If we take the unit a = 0.6 for the short side of the rectagon a very accurate value of Pi is obtained:
0.6 + 1.2 + 0.6 x sqr(5) = 3.14164
This is an amazingly close approximation of the value Pi = 3.14159, with the error of 0.0015%. Perhaps this is the reason why the two squares were frequently used for sacred devotional compositions, since the simplest proportions - two squares can easily be projected on the tracing board or simply in the sand - contain the infinite approximation of the Unity. It is to be remembered that this sacred places were used preferably by the High Priest in order to communicate with the divine in any form depending on the religious context. Whatever the method, from sexo-magickal rituals to the silent conversations from beyond, the main goal of such devotion devoid of sectarian religion was to destroy the self of the seer in the beloved in order to receive the Word that for the ancients held the universe together. Of course the reader must be warned that there is no known historical proof that the same interests were pursued in the King's Chamber of the Great Pyramid, on the contrary, the scientist utterly deny the possibility of magickal nature of the Pyramid, proving it to be merely a tomb for the pharaoh.
A very accurate approximation of Pi is obtained from the double square. The diagonal of such rectangle is a sgr(5), and the sum of the sides of rectangular triangle give very close number to Pi (a = 0.6):
0.6 + 1.2 + sgr(1.8) = 3.141640787 = Pi (error = 0.0015%)
Pythagorean Triangle in King's Chamber
Since the question arises if the builders used so precise measures while planning the floor plan of the King's Chamber, what happened to the height of the chamber, why not a simple whole number? Since all Biblical reflections would suggest the same height as is the width of ten cubits, thus obtaining a proportionally clean space of two cubes that seem so important in world's heritage, such a composition would not enable additional coding of information in proportions. The two cubes composition does not contain the Pythagorean triangle encoded, whereas slightly changed composition of the King's chamber does as previous researchers found out.
| dimension |
b. inch |
cm |
roy. cub. |
ratio |
palm |
digit |
| width |
412.5 |
1,048 |
20 |
4 |
140 |
560 |
| diagonal y |
308.5 |
783.5 |
15 |
3 |
105 |
420 |
| diagonal d |
515.1 |
1,308 |
25 |
5 |
175 |
700 |
Numbers 3, 4, and 5 play an important role in cabalistic heritage. To mention only the gematric value of Moses, MShH is 345, and God that introduced itself to Moses on the mount Sinai, while delivering the ten commandments, as AHIH AShR AHIH, or I Am That I Am, with the value 543. Even Hebrew alefbeth is structured via numbers 3, 4, and 5, since according to Sepher Yetzirah, alefbeth is divided in 3 mother letters, 7 (3 + 4) double, and 12 (3 + 4 + 5) single letters. The existence of the Pythagorean triangle in the composition of the King's Chamber also suggests that gnosis of Pythagoras comes from a much earlier source.
Volume of King's Chamber
The volume of the chamber is 19,510,260 cubic british inches. If we consider a simple cube that would occupy such volume, we find that this cube would have 269.2 b.i. for a side which equals 13 royal cubits. It seems that the symbolism of number 13 was very much intended. It was chosen as a basic cube from which the chamber is shaped, and it is the height of the chamber expressed in simple cubits of six palms. Such a principle of having a specific number of modules (calculii) for a side of a cube remained present in Pythagorean tradition. They called such cubes as metacubes, and even the word resembles a cube: Gk. METAKYBOS = 888. Additional message is conveyed by means of numbers that hidden or visible calculii represent. In the cube of 13 there are 469 visible calculi and 1,728 (12 x 12 x 12) invisible calculii.
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