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>>The mathematical key is the Fibonacci ratio. I think the references I saw
were to the Great Pyramid of Giza. ....Don't know of course if any of this is correct, <<
It's not.
The Great pyramids were created only after numerous prior attempts failed. Each successive attempt solved one additional engineering problem, and there were many. For example, if the slope was too steep, the walls would collapse outward. This was partially offset by sloping the stones inward and down, and partly solved by getting the right slope of the outside wall. Eventually, the best slope was found to be attained the following way.... You roll a huge wheel, say 20 feet high, across the land N complete turns. That specifies the length of one side of the pyramid. Next you lay 2*N wheels, edgewise, along the ground. (you really need only two wheels to do this, of course). The overall length spanned by this layout specifies the pyramid's height.
If the diameter of the wheel is D, then ...
base = pi*D*N, height = 2*D*N, and the width/height ratio = pi/2 = 1.571...
The Golden Ratio, which is the limiting ratio of the Fibonnaci sequence taken to infinity, is 1.618...
Although the two ratios are close, there's no cigar.
These pyramids were built 25 centuries BEFORE Cleopatra. They knew nothing about the value of pi or the Golden Mean. They didn't need to.
- Mark Jurik
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