E a r t h / m a t r i X
Science in Ancient Artwork

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Extract No.28

The Great Pyramid: Measurements

By

Charles William Johnson

The measurements regarding the Great Pyramid have always been under debate. Depending what, when, where and, how measurements were taken has produced conflicting measurements regarding the length of the base, slope and height of the Great Pyramid, as well as its angle of inclination. Given the fact that the Great Pyramid has not been in mint condition for millenia, it is understandable that such measurements have varied to the point of contradiction. The base measurement has been cited anywhere from 693 feet, through 756 feet, to 765 feet, depending upon which position is taken as the boundaries of the pyramid’s base. The pyramid’s height is impossible to measure exactly, given the fact that the capstone no longer exists. The pyramid’s angle of inclination has been computated as of a few stones found which possibly reveal the original angle, although again condition and the size of those stones make for calculations and not exact measurements.

Nonetheless, recently, measurements have been offered by the Director of the Giza Plateau Mapping Project, Mark Lehner, in a work entitled,The Complete Pyramids: Solving the Ancient Mysteries (Thames and Hudson, 1997). Let us examine the measurements offered in this scholarly work in the light of the numbers of the ancient reckoning system that we have been studying in the Earth/matriX: Science in Ancient Artwork series.

The base length of the Great Pyramid is calculated as 230.33 meters or 756 feet, according to professor Lehner, and its height once rose to146.59 meters or 481 feet (Ibid., page 108). The angle of inclination or slope of its faces are 51° 50′ 40″, again according to that same author. Much debate has revolved around employing measurements in the metric system or the English system; or, whether one should employ the numbers of the ancient cubit or, even some other unit of measurement. According to our reasoning, it does not matter which particular system of measurement is chosen for the discussion, given the fact that the geometrical outlay of the Great Pyramid allows for accomodating any system of measurement. This obtains from a comprehension of the mathematics of the ancient reckoning system and the very nature of geometry itself involving angles of inclination and the trigonometric table.

As we view the numbers offered by professor Lehner, we cannot help but immediately note that the metric measurement of 230.33 reminds us of the maya long count number 2304 (fractal), the alautun of 23,040,000,000. Nor can we avoid observing the possibility of relating the 146.59 measurement in meters to the Sothic cycle number 1460 or 1461 years. In most of our previous studies, we have employed the 756 feet measurement for the base length of the Great Pyramid, along with the 481 feet height measurement. The possibility of analyzing the angle of inclination has been dealt with previously by us (Cfr., Earth/matriX, Extract No.7, Pyramids of Egypt: Precession Numbers and Degrees of Angles).

Given the previously cited measurements, the following may be observed. The 51° 50′ 40″ angle translates into the decimal system as51.844444°, which when halved yields the number 25.922222. This particular number reminds us of the Platonic Cycle number of 25,920 years. Previously, we have discussed how the numbers of the angle of inclination of the pyramids of ancient kemi may have been reflecting just such a knowledge of the Precession. However, for computations in many of the ancient reckoning systems, it is widely held that the ancients avoided employing fractional numbers (with the exception of numbers regarding the reciprocal of seven). In this case, then, we might expect the angle of inclination to have been conceived (if not technologically achieved in the stone carving) as of 51.84°, or that of 51° 50′ 24″0 (a difference of 0° 00′ 16″0).

However, before we discuss such a variable, let us comprehend the relationship of the numbers offered by the Giza Plateau Mapping Project. The first question that comes to mind is whether or not it is possible, according to the trigonometric table, to obtain a pyramidal structure of the measurements offered. The answer would appear to be negative. Consider the following:

In Meters:

230.33
115.165²	+	146.59²	=	186.4178246²
115.165	/	.786336352 (sin 51.844444)			=	146.4576827	(a difference of .132317306 from Lehner’s datum)

In this case, the 146.4576827 appears to be more relational to a reciprocal of seven number: 146.4285714 with a lesser difference (146.4576827 – 146.4285714 = .0291113).

146.59 x .786336352

=

115.2690458 (a difference of .10404584 from Lehner’s datum)

In other words, it is impossible, trigonometrically speaking, to have a pyramidal structure with the given measurements of base length 230.33 meters, height 146.59 meters and an angle of inclination of 51.844444 degrees according to the posits of the Pythagorean Theorem.

In Feet:

756
378²	+	481²	=	611.7556702²
378	/	.786336352			=	480.7103208	(a difference of .289679234 from Lehner’s datum)
481	x	786336352			=	378.2277853	(a difference of .2277853 from Lehner’s datum)

In other words, it is impossible, trigonometrically speaking, to have a pyramidal structure with the given measurements of 756 feet base length, 481 feet height, and an angle of inclination of the slope of 51.844444 degrees.

The measurements of the Great Pyramid undergo such scrutiny because it has become a case of deciding whether the Great Pyramid was built with such great precision out of design or by happenstance. Although we are talking about an enormously, unimaginable monumental stone structure, at the same time we are considering the exact preciseness with which it appears to have been executed. Hence, the reason for considering the exactness of the numbers of the measurements. The numbers of the ancient reckoning system may assist us in comprehending the variations of the numbers offered in the current measurements.

The measurements of the Giza Plateau Mapping Project, which are admitted calculations, do not appear to conform to the historically significant numbers of the ancient reackoning system. However, if we allow for some adjustments of those numbers in terms of the ancient numbers, then the projected measurements and their adjustments appear to become more relevant.

If we allow for an angle of inclination of 51.84 degrees, the relationships of the numbers change. And, we must remember that if the angle of inclination remains as a constant, it does not matter which set of measurements for the length/height of the pyramidal structure is employed; the proportion remains constant in terms of trigonometry.

Adjusted numbers:

In Meters:

If 51.844444 degrees, but 230.4 meters:

230.4
115.2	/	.786336352	=	146.502193 (a difference of .087807005 from Lehner’s original datum)
115.2²	+	146.5111215²	=	186.3774362²

In Feet:

756 feet, but with 51.84 degree angle of inclination:

756
378	/	.786288432	=	480.7396174	(a difference of .260382556)
378²	+	480.7396174²	=	611.5509625²

or

481	/	.786288432	=	611.7348042
481	x	.786288432	=	378.2047358

611.7348042

-

481

=

377.9662295

( or, doubled to 755.932459)

Depending upon whether one begins with the baseline or the height of the Great Pyramid, the numbers change correspondingly.

There is another reason that one might want to consider the original angle of inclination designed into the Great Pyramid as having been 51.84 degrees. Consider the fact that if the baseline measurement of 756 feet is correct (the one that is most commonly accepted), then the following obtains:

378 x 51.84 = 19595.52We recognize in this fractal the Nineveh number of 195,955,200,000,000.

In the sine of the 51.84 number, .786288432, distinct ancient historically significant numbers appear: .786 (288)(432). Therefore, 288 being a maya fractal; 432, being the Consecration number.

Notice, however, when the 756 and 481 numbers given by professor Lehner are viewed in relation to the 360c of the ancient reckoning system:

481	/	756	=	.636243386
				.636243386	x	360	=	229.047619 458.0952381 916.1904762 1832.380952 3664.761905 7329.52381  14659.04762

146.59	/	230.33	=	.636434681
				.636434681	-	.636243386	=	.000191295 difference)

Whereas,

146.5904762 / .636243386 = 230.4000001

Hence, the baseline length of the Great Pyramid may be of any unit of measurement (230.33 meters; 230.4 meters; 756 feet; 500 cubits; etc.), with the angle of inclination remaining constant. Essentially, it does not matter even if one measures the baseline wrong; the angle pre-determines the proportional measurements of the triangle. This becomes even more evident when we employ the cited measurement of 500 cubits for the length of the base of the Great Pyramid:

In cubits:

500
250	x	51.844444	=	12961.111
250	x	51.84	=	12960/fractal (ancient kemi number 1296000)

An unsuspecting relationship developes from this possibility:

250²	+	317.9301063²	=	404.4496909²
		163579.5525	=	163579.5525

But, if we subtract this total amount from another ancient Sothic number (1649.457812 fractal) distinguished in previous Earth/matriX essays (Cfr., Essay No.73), the appearance of a number relational to the maya companion number obtains (1366560):

1649.457812

-

1635.795525

=

13.662287

Regarding any of the adjusted possibilities presented above, one could obviously obtain computations where the ancient historically significant numbers would become relational to one another.

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©1998-2006Copyrighted by Charles William Johnson. All rights reserved.

Your comments and suggestions are greatly appreciated:
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Earth/matriX
Science in Ancient Artwork
The Great Pyramid: Measurements 
Extract No.28
31 May 1998
^©1998-2006 Copyrighted by Charles William Johnson. All Rights Reserved

Earth/matriX,
P.O. Box 231126 New Orleans, LA 70183-1126; USA
Reproduction prohibited without written consent of the author.