Since there is no direct textual evidence to point to the design of Khufu’s Pyramid, I will examine the compositional relationships incorporated into the art and architecture of the Old Kingdom. We may then infer certain motivations by means of the ancient Egyptian religion, aesthetics and use of proportion. In general, in an overview for assessments of intention for architectural authorship in ancient Egypt one can conclude that golden ratio related geometrical figures and mathematical relationships could be found (Rossi 2004, 32–56, 86]. Without doubt, there are difficulties encountered with any singular theory applied to the architecture of ancient Egypt but one in particular has gained some credibility. Of course, any a posteriori attempts to deduce a plan is always speculative, but in measuring 55 Egyptian temples there was consistent evidence of a simple golden ratio proportion (1:1.6) by applying a 5:8 isosceles triangle to the plans (Badawy 1965, 19–40).Footnote 4 Furthermore, an investigation over 12 years at Luxor Temple demonstrated that its architectural plan was rigorously based upon Egyptian aesthetic proportions of the figure and corresponded to vital anatomical parts of the body, especially the navel. The use of golden ratios was also quite evident (Schwaller de Lubicz 1998, 66).

Undoubtedly, artists and architects through the ages, especially Greek sculptors and particularly the architects Vitruvius and Le Corbusier, have presented us with their versions of the ideal canons of human proportions. It is well documented that Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural design. He saw his system as a continuation of the long tradition of Vitruvius.

Modern Egyptologists agree that the pharoanic rule of proportion for depicting the standing human figure used a modular system of 18 squares from the soles of the feet to the hairline, (thus allowing for various heights of crowning head-dresses). The navel (the important symbol of maternal attachment, birth, and continuity) was placed just above square 11 (or about 11.1) and clearly seen in Fig. 2. This proportion, 18:11.1, is an excellent approximation of Φ. The navel divides the height of 18 squares by a proportion of about 11:7. By combining the septenary unit (based on the royal cubit of seven palms) and the factor of 11 the ancient Egyptians were easily able to solve a number of practical geometric calculations. Incidentally, the numbers 7, 11 and 18 are also in a Fibonacci-like (Lucas numbers) summation sequence of 1, 3, 4, 7, 11, 18… (Fig. 3). It is also interesting that the vertical grid line through the eye and navel bisects the triangle of the Pharaoh’s apron, perhaps a significant reflection of the shape of the pyramid as well as an obvious center of procreative continuity.Footnote 5

Fig. 3 Standing figure on the original grid in KV22 of Amenhotep 11, after Robins (1994, 46) Full size image

Well known for his 1992 Upuaut robot investigations of the ‘airshafts’ and the discovery of a ‘door’, Gantenbrink (1997), also found 14:11 and 11:7 proportions evident in interior measures and in the horizontal exit points of the ‘airshafts’. Actually, these are not airshafts, but believed to be symbolic exits for the Pharaoh’s ka (spirit) to reach the after-life and return to the mummified body at will. Many consider these shafts astronomically or cosmologically important, or perhaps, simply as sightings to guide the construction. Whatever their function, they must have had very special significance for the builders to incorporate diagonal tunnels through successive layers of tons of horizontally laid rock. They are placed at a 14:11 division of the vertical height. This proportion would give a pyramid angle of 51.843°, virtually the same as the observed angle of 51.844° (Fig. 4).

The square grid proportion of the Egyptian sitting figure is 14 squares high with the navel at 7 squares. If we compare this to the side elevation of the pyramid, we can see that it perfectly matches the 11:14 proportion of the exit heights of the shafts. The crown of the figure at square 14 matches the exit heights of the shafts. Significantly, the navel at square 7 aligns with the position of the Royal burial chamber. Similarly, the airshafts meet at a point at the base of the Royal burial chamber that is 11/18 of the horizontal distance between the outer openings of the two shafts. If we position the standing figure on its side to correlate with the prone position of the Pharaoh’s mummy, then the offset Royal burial chamber is exactly in vertical alignment with the navel of the standing figure (Fig. 5). This offset from center of the Pharaoh’s chamber has been puzzling to many, especially since the so-called Queen’s chamber below is at a perfect center. The significance of the modules of 7:11 rectangles is hereby explained. The alignment of the navels of the sitting and prone figures perfectly determine the location of the burial chamber, the raison d’etre of Khufu’s Great Pyramid.