The angle according to Petrie and others [donbarone.altervista.org] IS NOT 31 degrees. When this fails the house of cards comes crashing down.

If height is 9 cubits and width is 10 cubits and apex is 12 cubits the best we can get is 3/5 = 0.6 and angle that has a tan of 0.6 is 30.964 (rounded off)

Unfortunately Petrie does not agree with any of this. Here is what he says about the angle of the supporting megalithic blocks:

[donbarone.altervista.org]

As you can see none of the values check. Petrie has the slope in his first example at 120 inches but that would mean (using 20.62 inches per cubit) that the slope is 5.8196 cubits (rounded off). The second example has the slope length at 119.96 inches. This equals 5.81765 cubits (rounded off).

The diagonal of G2 allowing base and sides to equal 411.035 gives us 581.29127 (rounded) this when divided by 100 and then multiplied by 20.62 gives us a slope length of 2.81.29127 x 20.62 = 119.86 inches and well within the tolerances that Petrie found. Assuming that 9 cubits was correct for the height and 10 cubits was correct for the width to solve for height to apex we need 581.29127/100 or 5.8129127 squared minus 5.0 squared and we get 2.9648 (rounded off) and added to 9 we find apex seems not to be 12 but 11.9648 cubits.

If we want to insist on 31 degrees we get height to apex of 9 + 3.0043 or 12.0043. Slope becomes 120.27 inches. It seems like at lot but for heaven's sake it is only 1/4 or an inch more than the value Petrie got.

I really wonder if we will ever know what was intended by the builders/designers. Using 2.9648 and dividing by 5 we get a top angle of 30.666 degrees. [tan of 30.666 = 2.9648 / 5 = 0.592957 (rounded off) ]

The more I think on it the more I believe Pi and Phi and 31 degrees was the intent with the following measurements:

Deflection angle of roof: 30.99987566446 ( rounded off )

Ratio of slope to added on height: Phi / Pi or 0.5150362148 (rounded off). This is sine of 30.99988 (rounded off) degrees

Ratio of the two sides: 3.0043 / 5 or 0.60086. This is tan of 30.99988

and finally

slope distance is Phi / 2.692874 (rounded off) x 5 = 1.166632 (rounded) x 5 = 5.83316 (rounded) x 20.62 = 120.28 (rounded off) inches

Yes, this seems to fit the best.

db

"There is nothing as impenetrable as a closed mind"
and ..." if everything is a coincidence what is the point of studying or measuring or analyzing anything ?" db