Many thanks all, the wiki golden ratio material shows how this perimeter pi derivation is controversial. The Emerald Tablets of Thoth are a document which Sir Isaac Newton translated into English. Newton's version gives this document as the source of the hermetic idea 'as above so below'. The pyramid builders revered Thoth as the founder of astronomy. I am simply intrigued by the possibility that, having apparently incorporated the perimeter/pi ratio in the slope to the capstone, they followed this through by preparing the foundations of the construction to form an octahedron, with the pyramid above reflected in a pyramid below ground, but I have no evidence for this. A claimed history of the emerald tablets is at http://www.alchemylab.com/hyper_history.htm