Science in Ancient Artwork

Extract Nș 7

Pyramids of Egypt:
Precession Numbers and Degrees of Angles

Charles William Johnson

One of the most intriguing aspects of the pyramids of ancient Egypt appears to be the distinctive degrees of their angles of inclination. The precision with which most of the ancient pyramids were made is reflected in the number of degrees chosen. Aside, then, from the preciseness of the technical execution of the masonry work in which stones were placed together with unimaginable exactness; aside from the placement of the Great Pyramid regarding the north-south coordinates of the Earth; one can only marvel at the distinctive angles of degrees employed in those ancient structures. Numerous discussions and interpretations exist as to why specific degrees were chosen. None seem to be possibly related to the reasons behind why the ancient architects chose those particular degrees of inclination.

In our analysis of the logic of the numbers of the ancient reckoning systems, we have been attempting to view how the numbers may relate to one another; often, outside of the normal ways in which the numbers have been identified or interpreted. The numbers may suggest by themselves a specific method of computation through their possible relationships, and thereby may even be suggestive of some of the meanings that the ancients may have assigned them. The numbers of degrees of inclination of the pyramids of ancient Egypt suggest a direct encoding of the numbers related to the Precession of the Equinoxes as we shall examine herein.

Degrees of the angle of inclination in the pyramids have been expressed indiscriminately over the years, either in decimal degrees (52°) or in degrees-minutes-seconds (52° 00' 00"0), causing at times confusion in certain comparisons. The possibility may exist whereby the numbers expressing the Precession (26000), when viewed as fractals may be translated into the 60-based system of degrees (26° 00' 00"0). If such a relationship existed in the numbers, then one might safely conclude that the degrees encode the numbers of the Precession. The numbers we have chosen in the previous examples do not offer much insight into this possibility. Therefore, let us examine distinct numbers that have been cited in the historical record for the Precession in different ancient cultures, alongwith distinctive numbers that have been cited for angles of inclination in the ancient pyramids.

Some of the most commonly cited numbers representing the number of years of the Precession are 26,000 (The Great Sun Cycle); 25,920 (The Platonic Year); and, 25,956 (The Maya Precessional Number). Many others exist. Some of the more commonly cited degrees of inclination, that is, the angle of rise of the faces of the pyramids to the horizon, of the pyramids of ancient Egypt, are: 52° (The Perfect Pyramid at Meidum); 51° 50' or 51° 51' 14" (among others of The Great Pyramid of Khufu); 52° 20' 00"0 (Second Pyramid of Giza); 51° (Third Pyramid of Giza); among many other distinct degrees of inclination for the pyramids throughout Egypt, which appear to range from 42° 59' 26" (Southern Stone Pyramid of Dashur) on up to 75° 20' 0" (Pyramid of Rigah).

From the previous sets of numbers, the obvious point is that the Precession numbers are expressed on the decimal system of 10s, 100s, 1000s; while the numbers of the degrees of angles are on the 60, 180, 360 based system of a circle. One may translate the decimal-based system numbers (i.e., 26,000) into the 60-based system of numbers (i.e., 26° 00' 00"0). Even contemporary pocket electronic calculators have a key (DD>DMS) for this function. One might not expect a direct relation to exist between one system of numbers and another in terms of the encoding of the Precession numbers; but this may be the case as we shall observe immediately below.

First, let us remember the method of doubling/halving the numbers that was used in ancient Egypt (kemi). Consider the ideal case of the Precession number 26,000 years:

104, 52, 26, 13 are significant cycle numbers of ancient Mesoamerica. These numbers may be easily translated into the 60-based system: 26 would simply be 26° 00' 00"0, for example, while 52 would be 52° 00' 00"0. Now, let us see what the relationships would be if we considered the different numbers of the Precession and the angles of inclination of some of the pyramids of the ancient world.

The Platonic Year 25,920 would produce the following numbers:

103.68; 51.84; 25.92 expressed as fractals of the decimal system. Therefore, 51.84° is 51° 50' 24"0. In other words, the angle of inclination 51° 50' 24"0 would express the decimal number 51.84° , which could be the fractal expression of double the 25,920 Platonic Year number (25920 x 2 = 51840). These numbers and degrees would represent the ideal grand cycle of the Sun of 26,000 years.

103.7; 51.85; 25.925 would be the expression set for an angle of inclination of 51° 51' 00"0, since these numbers reflect 51.85° , when expressed in the decimal system.

103.708; 51.854; 25.927 would be the expression set for an angle of inclination of 51° 51' 14"4, or 51.854° , thereby representing the fractal double of the 25927 precession number. This would mean that the angle of inclination cited by Piazzi Smyth (THE GREAT PYRAMID, p.436) of 51° 51' 14"3 would reflect the decimal number 51.85399° or this fractal halved to that of 25,926.995 years (51,85399/2=25,926.995).

The ancient maya are cited as having employed the Precession number 25,956 years (Harleston: EL UNIVERSO DE TEOTIHUACAN). This number would then be expressed as follows: 25.956; 51.912; 103.824, or in other words, 51.912° would represent an angle of inclination of 51° 54' 43"2. One immediately observes how these numbers suggest those of 51 degrees; 54 minutes, reflecting the ancient kemi series of 27, 54, 108; and, 432 the number of Consecration found through many ancient cultures.

Pyramids of ancient Egypt exist with angles of inclination of 54 degrees, which would suggest a precession number of 27,000 years: 108, 54, 27. While the pyramid of Abuseir with its cited angle of inclination of 51° 42' 35" would reflect a precession number of 25,850.005 years (whereby 51.70001° represents that particular 60-based system number; and, 51,700.01/2 = 25,850.05). This particular numerical expression is closer to the figure used today for the Precession of the Equinoxes, around 25,800 years. The degreee of inclination for the northern brick pyramid of Dashur cited by Smyth, 51°20'25" would represent a lower count, since this number would reflect 51.34027778° (decimal expression) or half that, a 25,670.138889 precession number.

The case of the number often cited for ancient Nineveh also yields an interesting combination. By continuously dividing 1959552 (fractal expression) by 2, we reach the number 15309, which must then be divided by the number 3 given it ends in an odd number (9): 15309/3 = 5103. This suggests the series 102.06; 51.03; 25.515. The number 51.03° would be 51° 01' 48"0; reflecting the precession number 25,515 fractal. This particular number may be viewed distinctly: 25515 - 25920 = 405, 810, 1620, 3240, 6480, 12960, 25920 (the Platonic number again). Or, if we subtract 405 progressively from 25515, we reach the number 22680, another significant number cited for Nineveh.

Now, if we look at an historically significant number of the ancient maya, the companion number 1366560, and divide it progressively by 2, we reach the number 21352.5, which would be an extremely low number for the precession. Yet, by following the same procedure, 21352.5; 42705; 85410 would suggest an angle of inclination of 42° 42' 18"0 (= 42.705° ). Interestingly enough, the Pyramid of the Sun of Teotihuacan, among others in ancient Mesoamerica, reflects angles of inclination around 43° (i.e., 41.4° to 43.35° ). Another companion number of the maya is 1385540, which would be halved progressievly to 43298.125, an angle of inclination of 43° 17' 53"2. One cannot help but notice that the cited 43.35° angle would yield an angle of inclination of 43° 21" 00"0, again making its appearance the 432(1) fractal of the consecration. Or, consider 43350/ 2 = 21675 and, 26000 - 21675 = 4325; again, the 432(5) fractal.

Other seemingly odd translations involve numbers such as the k'awil (819c) of the maya. Whereby 81.9° translates into 81°54' 00"0. Immediately, we see appear the fractal numbers of the 25920 Platonic Year appear in an inverted manner. Remember, the 25920 Platonic Year suggests an angle of 51.84° (8154:5184). This inversion of fractals appears to have been present in the ancient reckoning system. The number 576 was significant for the ancient maya; 756 appears to have been in the ancient kemi system; 819 for the maya, and 189 for the kemi; among many other examples.

One may consider, then, the possibility that the angles of inclination may have reflected the numbers of the Precession of the Equinoxes as we have shown above. If we consider that the distinct numbers reflect distinct computations, whereby many different individuals were attempting to calculate the number of year corresponding to the Precession of the Equinoxes, such a wealth of numbers might then be explained. Aside from different individuals calculating different figures for the Precession, one might also consider their having chosen different percentages or periods for the Precession (hence, the distinctive degrees of the Mexican pyramids).

Precession Number Angle of Inclination
27000 posited 54° 00' 00"0
26100 posited 52° 12' 00"0
25956 MAYA PRECESSION NUMBER 51° 54' 43"2
25933.333 projected 51° 52' 00"0 The Great Pyramid (Hancock)
25927 projected 51° 51' 14"4 The Great Pyramid
25926.995 projected 51° 51' 14"3 The Great Pyramid (Smith)
25926.944 projected 51° 51' 14" The Great Pyramid (Smyth)
25925 posited 51° 51' 0"0
25920 PLATONIC YEAR 51° 50' 24"0
25714.28 Reciprocal of 7 derived 51° 25' 42"8
25515 NINEVEH derived 51° 01' 48"0
21675 projected 43° 21' 00"0 Teotihuacan; Pyramid of Sun
21352.5 projected 42° 42' 18"0 1366560 derived

Adjustments may have been in all of these options. Consider, if one subtracts 7 years from the 25515 Nineveh number for the Precession, the following obtains: 25508, or 51.016° , or 51° 00' 57"6; 576 being a maya fractal. In this manner, increments/decrements could be based on the maya long count numbers.

The kemi system and the maya system appear to flow one into the other at this level of analysis. The historically significant numbers appear in many different and possible combinations. But, the surprising point would appear to be the manner in which numbers and degrees expressed either as decimals or as of the 60-based system reflect two specific realities: the numbers referring to the Precession of the Equinoxes cited in the historical record, and the angles of inclination of the ancient pyramids of the kemi and the maya. As we have seen in this brief analysis, the degrees of angle of inclination found in the faces of the ancient pyramids reflect the double fractals of the numbers of the Precession with strict logic.

Due to the wear of the faces of the pyramids, and the difficulty of measuring them, the precise measurements of the angles of inclination have never been agreed upon by archaeologists. But, one could easily imagine in theory that the ancient system may have been based upon the considerations pointed out in this analysis, whereby the historically significant numbers may have appeared symbolized in the different sets of numbers shown here. The very logic of the procedure would allow for this without difficulty. In any case, there is a direct relationship in the translation of the Precession numbers into the numbers of degree-minutes-seconds of the angles of inclination of the faces of the pyramids.

©Copyrighted 1997-2012 by Charles William Johnson
Reproduction prohibited without written consent of the author.


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Science in Ancient Artwork
Extract Nș.7
Pyramids of Egypt: Precession Numbers and Degrees of Angles
21 April 1997
©1997-2012 Copyrighted by Charles William Johnson. All Rights Reserved
Earth/matriX, P.O. Box 231126 New Orleans, LA 70183-1126; USA

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