Pyramid Geometry

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The dimensions of the Great Pyramid of Giza possess some fascinating connections. Pi (π) is defined as the ratio of the diameter of a circle to its circumference (3.14159265...). The Fibonacci number (phi) is derived from the sequence 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610... where the sum of two preceding numbers gives the next number in the series. One number divided by the previous value moves towards phi and becomes ever closer to (approx) 1.618033989: or (√5 + 1 )/2. But why √5 and not some other relationship? But... it works and is therefore empirical as an irrational number (π is an irrational number). These two constants (π and phi) are related and appear in the pyramid shape. This combines the dimensions of the circle with the triangle.

One-half the base width (a =  ...144, 233, 377...) and the corresponding slope [hypotenuse] (h = ...233, 377, 610... ) provide the angle θ (144/233, 233/377, 377/610... a/h = a constant nearing 0.618034). In terms of the trigonometric ratio, arccos θ = 0.618034 gives θ = 51.83º. This is the angle of the pyramid slope. The height (o) for a base pyramid base width of 754ft yields a x tanθ or height = 377 x 1.2729 = 479.9ft. The value of π = 4a/height (1508/479.9) = 3.142 and this always applies: eg a = 144 and h = 233 (a/h = 0.618) gives height as 233 x 1.2729 = 296.586ft or π = (233 x 4)/296.586 = 3.14242749...

• All the values are (rounded-up) approximations