Geometry of the great Pyramid
By Nick Kollerstrom Phd

The three Giza pyramids are located at 30° North, within an arcminute. (1)

The sides of the Great Pyramid point North within two or three arcminutes. (2)

Its slope angle is closely one-seventh of a circle, i.e. 51.4°.

More exactly, it is given A when cosA = 1/Φ where Φ is the golden ratio. So slope angle is 51° 50'.

A 'golden triangle' defines the slope angle, with sides 1 for the base, √Φ for its height and Φ for its long side (hypotenuse); thus its sides increase or 'grow' in the same proportion.

We may write the 'Pythagoras' theorem' of this right-angled triangle as, Φ² = Φ +1. That was two thousand years before Pythagoras.

Diagram reproduced with permission from Heaven's Mirror by Graham Hancock and Santha Faiia

This implies, that the square on the height equals the area of a pyramid side. To make a replica of the Great Pyramid, draw a 'map' where two golden rectangles are added to each of the four sides, and the pyramid sides drawn as triangles upon them.

The slope angle is also such that tan A = 4/л, i.e. the square on the base has length equal to that of a circle perimeter, whose radius equals the pyramid height: 51° 51'.

Thus phi and pi are integrated at this unique slope-angle. The four sides in fact concur within about an arcminute, on this slope angle.

The pyramid height is 280 royal cubits and its base 440, so base to height are in the ratio 11 to 7 - an early expression of the л- ratio? Here, tanA = 14/11 giving 51° 51.'

The 'King's Chamber' has its length twice its breadth and its height is half the diagonal of that rectangle.

Taking the width of this chamber as unity, phi Φ is traced out by the height plus half the width.

A 3:4:5 Pythagoras triangle is contained in the diagonal plane of this otherwise-empty chamber: if its length is 4 units, the main diagonal is 5 and the diagonal across the end wall, 3.

The actual size of this integer Pythagoras triangle in the King's Chamber establishes the units used for the Great Pyramid's exterior; the triangle sides being exactly 20, 15 and 25 royal cubits.

Notes:

1. This 1' error may have been due to atmospheric refraction: Peter Lancaster-Brown, Megaliths, Myths and Men, 1976, p271. 'The apparent (not true) altitude of the pole is 30° 00' (1/12 of a circle) as seen from all three Giza pyramids:' Dio, a history of astronomy journal, Baltimore, Dec. 2003. Hugh Thurston, 'Orientation of Early Egyptian Pyramids', p.6. [back to text]
2. For comparison, the adjacent Khafre pyramid points due North with an error of about 6', but in the other direction, possibly indicating a later construction. [back to text]