This came up on another topic, and this is a more appropriate place to discuss the mathematics.

The measured slope of the Grand Gallery is 26 degrees 17 minutes or thereabouts.

If the build standard was accurate to 1 part in thousand then the slope should be this angle plus or minus 3 arc minutes, which corresponds to a rise of 28 digits and a run somewhere between 56.57 digits (14.14 palms) and 56.82 digits (14.21 palms), using decimals for analysis. ie to determine whether or not any proposed angle is in the required range.

NB This is not the same as the slope proposed for the Ascending Passage which is well outside this range.

I have proposed that the intended run was (sr360/sr88) x 28 digits = 56.63 digits which is in this range, and where:

88 digits is the width of the Grand Gallery between the third laps as pi royal cubits

and

88 royal cubits is the floor length of the Grand Gallery.

Fig 12 on page 78 of my monograph on the Grand Gallery explains why:

Take 88 royal cubits as the the base of a triangle along the central axis of the gallery.

Take 14 royal cubits as the short side of the triangle, from the foot of the Great Step to the pole of the pyramid.

The hypotenuse is very close to 89 royal cubits 3 digits

Area of triangle = 1/2 x 88 x 14 = 616 square royal cubits

The triangular cross section of G1 equates to 1/2 x 440 x 280 = 61,600 square royal cubits

A circle with a diameter equal to the height of the pyramid has the same area:

1/2 x circumference x radius

1/2 x 880 x 140 = 61,600 square royal cubits

The slope of the Grand Gallery squares the circle, and the circle represented has a radius of 140 royal cubits, a diameter of 280 royal cubits, and a circumference of 880 royal cubits:

The triangle latent in the design of the Grand Gallery is a 10:1 scale model, as are elements of the Queen's Chamber, and represents the formula for the area of a circle.

But where can we find the hypotenuse to prove this was intended?

The roof is longer than the sloping floor by 31 digits which is 89 royal cubits 3 digits.

Mark



Edited 1 time(s). Last edit at 12/06/2012 11:46AM by Mark Heaton.