I have been investigating a curious style of geometry for some time now, and recently I have been applying it to the Giza layout. While I was doing this something showed up that may be of some interest here.
This is the basic floorplan for the Great Pyramid(GP1). I'm not going to quibble about the nitty-gritty of the exact measured sizes found by todays methods. This is an exercise in this particular style of geometry, and it's possible links to ancient monuments. For this purpose I am assuming the side length is exactly 756 feet. It's easy enough to apply the resulting ratios to any sizes you may prefer.
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All this geometry is compass and square edge, so you can assume that no other instruments are needed. All these diagrams are constructed on C.a.R Metal, a free geometry program, but they can all be hand drawn too, at least until the point that drawing error gets too much. I have omitted almost all the construction lines for clarity.
This second diagram adds two arcs, with the square diagonal as the radius, drawn from both bottom corners of the square. The point where they meet is 1000.094 feet from the square's baseline. Up to this step all came from a British Neolithic site, the rest has come from Giza.
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If the bottom corners are now joined to this intersection it forms what I think is a pretty good impression of a Nubian pyramid. The quoted slope angles given to these pyramids are in the range of 68 to 72 degrees, with the oldest known having a slope angle of about 69 degrees. The triangle below has an apex angle of 41.4 degrees, so it's slope angle is 69.3 degrees.
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I think this little exercise fits this quote I pinched off Dune's thread really rather well...
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In a further development to this geometry the square is doubled downwards which makes the construction look like an arched doorway....
One other thing, the ratio, in the further development, works out to be the square root of 7...
cloister
This is the basic floorplan for the Great Pyramid(GP1). I'm not going to quibble about the nitty-gritty of the exact measured sizes found by todays methods. This is an exercise in this particular style of geometry, and it's possible links to ancient monuments. For this purpose I am assuming the side length is exactly 756 feet. It's easy enough to apply the resulting ratios to any sizes you may prefer.
All this geometry is compass and square edge, so you can assume that no other instruments are needed. All these diagrams are constructed on C.a.R Metal, a free geometry program, but they can all be hand drawn too, at least until the point that drawing error gets too much. I have omitted almost all the construction lines for clarity.
This second diagram adds two arcs, with the square diagonal as the radius, drawn from both bottom corners of the square. The point where they meet is 1000.094 feet from the square's baseline. Up to this step all came from a British Neolithic site, the rest has come from Giza.
If the bottom corners are now joined to this intersection it forms what I think is a pretty good impression of a Nubian pyramid. The quoted slope angles given to these pyramids are in the range of 68 to 72 degrees, with the oldest known having a slope angle of about 69 degrees. The triangle below has an apex angle of 41.4 degrees, so it's slope angle is 69.3 degrees.
I think this little exercise fits this quote I pinched off Dune's thread really rather well...
In a further development to this geometry the square is doubled downwards which makes the construction look like an arched doorway....
One other thing, the ratio, in the further development, works out to be the square root of 7...
cloister