Let’s have a look at some numbers for the Great Pyramid.
Source: Building the Great Pyramid (aka Cheops)
Copyright 2006 Franz Löhner and Teresa Zuberbühler
Dimensions as designed (in Egyptian royal cubits):
Original dimensions as built (a,h and c in the pyramid diagram below):
Length: 230.36m (half = 115.18m)
Consider the right-angled triangle formed by half the length, the height and the slope. In the diagram the right angle is in orange with a black dot in it.
In Egyptian cubits the triangle sides are: 220 (length = 440/2), 280 (height), 356 (slope).
Using the design numbers, the proportions of the sides of the triangle are:
Length:slope = 1:1.61818 (18 recurring)
Length:height = 1:1.2727 (27 recurring)
Phi = 1.6180339~
Square root of Phi = 1.2720196~
Using the dimensions as built, the proportions of the sides of the triangle are:
Length:slope = 1:1.61851
Length:height = 1:1.2727035
Wikipedia says: ‘A Kepler triangle is a right triangle with edge lengths in geometric progression. The ratio of the edges of a Kepler triangle is linked to the golden ratio…approximately 1 : 1.272 : 1.618. The squares of the edges of this triangle are in geometric progression according to the golden ratio.’ [link has a diagram].
Löhner and Zuberbühler say:
‘Pyramid angle α = 51° 50′ 40″ = inclination of the lateral surface.’
For an exact Kepler triangle, the angle should be about 51° 49′ 38.25″ (= 51.8273°). In this diagram we have 51.83°.
goldennumber.net says: ‘Although difficult to prove due to deterioration through the ages, this angle is believed by some to have been used by the Egyptians in the construction of the Great Pyramid of Cheops.’