Phi and the Great Pyramid of Khufu

(Before It's News)

Great Pyramid of Giza from a 19th-century stereopticon card photo [credit: Wikipedia]

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):
Length: 440
Height: 280
Slope: 356

Original dimensions as built (a,h and c in the pyramid diagram below):
Length: 230.36m (half = 115.18m)
Height: 146.59m
Slope: 186.42m

Dimensions of the pyramid of Khufu
[credit: Franz Löhner and Teresa Uberbühler]

Consider the right-angled triangle formed by half the length, the height and the slope. In the diagram [click to enlarge] the right angle is in orange with a black dot in it.
In Egyptian cubits the 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].

The angle of 51.83° (or 51°50′), has a cosine of 0.618 or phi
[credit: goldennumbers.net]

Löhner and Zuberbühler say:
‘Pyramid angle a = 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.’

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