That is exactly equal to 7,623 12-cubit cubes; cubes, that is, of surface area equal to that of the theoretical metrological cavity. Now, these 7,623 cubes can be arranged as a stack of 7 equal square tiers of width 33. With the width of the tiers equal to the width of the base of the pyramid, the height of the resulting rectangular block is exactly 1/3rd of the height of the pyramid. Altogether, the figure clearly embodies in whole numbers the arithmetical method for calculating the volume of any pyramid; one third of the height times the area of the base.

Hence it may be concluded that the Horizon Pyramid was laid out and constructed using the pyk belady as its modulus. However, because nothing is known about the history of this unit of measure beyond its use in the construction of the Horizon Pyramid and its general use in Egypt at the time of Jomard's visit, its age and origin cannot be established and, therefore, no firm conclusion can be drawn about the age of the Horizon Pyramid from its use. Jomard's observation is seemingly the only connection to any memory of its existence, since all other mentions of this unit themselves refer back to him as their source. Nonetheless it is clear that the linear modulus of the Horizon Pyramid possesses a unique name and is no mere hypothesis. Not only that but the Horizon Pyramid linear modulus can confidently be labelled the Egyptian cubit, for that indeed is what it is.

Figure 3-8. The Egyptian Stade

Taking the disk of the Earth as a circle and the value of pi as 22/7, in Egyptian stades of 400 cubits the circumference so obtained is exactly 171,072 Egyptian stades and the radius 27,216. A Greek stade on the same circle would be exactly equal to 99/125 Egyptian stade (terrestrial circumference = 216,000 Greek stades).

The Horizon Pyramid width, at 99/100 Egyptian stades, is equally interesting since the terrestrial circumference comes out at 172,800 or 100 times the cube of 12. Moreover, again on the same circle, it is exactly equal to 1¼ Greek stades, the Greek metric standards having been supplied to Solon by the Temple of Neith at Sais around 600 BC, suggesting an unbroken tradition stretching from the building of the Giza complex to that of the Parthenon of Athens. The Greek system of linear measures was derived from the Egyptian and both include a digit (finger) as the smallest unit, a foot of 16 digits, a cubit of 24 digits and a stade of 600 feet.

* Peter Tompkins' website was removed from the World-Wide Web in February 2008, a year after his death in January 2007. This author has a copy saved in his archives.

3-3. The Grand Pyramid

The mean width of the base of the Grand Pyramid is almost exactly 370 Horizon cubits (pyk belady), the variance being roughly 1 part in 6,000 or 0.016%, and here the rounded figure will be assumed to be the intended width. This pyramid was apparently intended to conform to the proportions of a Pythagorean {3-4-5} triangle, giving a theoretical height of 246⅔ cubits or 370 feet.

Figure 3-9. Theoretical Cross-Section of The Grand Pyramid

The theoretical volume of the Grand Pyramid is exactly 37,989,750 cubic Horizon feet.

37,989,750 = 2 × 3 × 5³ × 37³ = 6 × 185³

The length of each edge of the 6 cubes so defined is equal to half the height of, and to one third the width of, the pyramid.

3-4. The Divine Pyramid

Petrie's mean for the width of the Divine Pyramid is 4,153.6 English inches, or roughly 181.34 Horizon cubits with a probable intended figure of 181⅓ cubits, or 272 Horizon feet exactly, differing from the mean by ­­­­­–0.004%. For the angle of the apothem Petrie's “best conclusion” is 51°0' ± 10'. This results in a height somewhere between 2549 and 2580 English inches, or roughly 167 and 169 Horizon feet. Taking the mean gives a height of 168 feet and this will be found to share a common factor of 8 with the theoretical width. Hence the proportions are 21 rise on 17 base, revealing a clearly intended allusion in the division of the width by the height to Φ (Phi), the Golden Mean or Divine Proportion, differing from it by a mere +0.06%. In fact the ratio of height into width, 21:34, displayed by the Divine Pyramid is the 8th term of the Fibonacci Sequence, which converges to Phi.[18]

Figure 3-10. Theoretical Cross-Section of The Divine Pyramid

The theoretical volume of the Divine Pyramid is exactly 4,143,104 cubic Horizon feet.

4,143,104 = 7 × 34² × 8³

* * *

Figure 3-11. The Ratio between The Heights of Horizon And Divine Pyramids

The ratio between the heights of Horizon and Divine pyramids is the same as that between the length and breadth respectively of the platform of the Parthenon of Athens - 4:9. This ratio belongs to the Lambda, itself the root and source of the dodekaphonic musical scale, as described in Chapter 1, suggesting that the Giza complex comprises an integrated design and that its overall planning was completed before a single stone was quarried for a single pyramid.

Figure 3-12. The Pyramids of Giza (2)

3-5. The Southern Shining Pyramid

Figure 3-13. The Southern Shining Pyramid

The reader can forget the Egyptological dogma that seeks to explain the compound slope of the Southern Shining Pyramid as a decision by the builders to switch slopes in mid-project, the rationalization of this usually being that they discovered that the internal stresses of the structure prevented completion of a pyramid with the continued slope of the lower section. How exactly they discovered this is never made clear and no evidence supporting the stress-factor hypothesis is ever presented. It is of course a flight of fancy, for from the outset the Southern Shining Pyramid was designed to be a flattened obelisk, as the following analysis of its geometry will make very clear.