## Floor Plan Geometry

 Figure 1: The Great Pyramid: Section. The Great Pyramid There appears to be a widely-held view that the length of the slope at centre of the face of the Great Pyramid (G1) has a phi relationship with half the base, meaning that the slope is in the region of 356 Royal Cubits. This would imply that the square root of five is 123/55, a remarkably accurate estimate, but did the builders know this and would this be consistent with the pyramid’s internal dimensions, particularly those of the King’s Chamber? Figure 2: Potential Geometry of King's Chamber Floor Plan. The King's Chamber Floor Layout The floor plan of the chamber is significant in being twice as long as it is wide, that is, 20 cubits by 10 cubits. This might immediately draw attention to the possibility that phi is present in the design, because this is calculated as (the square root of five plus one) divided by two which can be illustrated geometrically, as shown in the figure. Of note is that a chord of the circle between the north and south walls defines the phi location at the centre of the outer circle (point E). Figure 3: The King's Chamber Floor Plan and Sarcophagus. Geometry and the Sarcophagus Knowing this, a similar construction may be applied elsewhere on the plan, as shown in the figure, but the key design is at top left which, in combination with the main circle, produces the rectangle in grey. This measures 2 by 4.47 cubits, or 56 by 125 digits. Suppose that this is the intended size and positioning of the lid of the sarcophagus and that the cover overlapped the edges of the coffer by 2 digits all round. Thus, with a height of 1048mm as two cubits, the sarcophagus would measure 2265mm by 973mm. If the physical location of the sarcophagus matches the construction accurately then this may well be a pointer to the Ancient Egyptians’ knowledge of phi and also of its derivation. It implies that the square root of five may have been considered to be 56/25 (2.24) and that phi would be 81/50 (1.62). On this basis, the slope of the pyramid would be calculated as 356.4 cubits, without the indentation. Rounding would simply render the ratio more accurate. © G.J. Bath, 2020

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