an answer finally came from an astronomer about the moon within a tetrahedron
within the earth scenario. Someone on here proved it wrong because they were
using a triangle and not a tetrahedron. read on...
Don Barry:
If memory serves, the size of a sphere inscribed within a tetrahedron
inscribed within a sphere is that of one quarter the radius of the
external sphere. And the Moon is roughly one quarter the radius of the
Earth. There is no physical relationship between the two: neither the
Moon nor the Earth is a perfect sphere, and the relationship isn't
exactly a 1:4 match. But pick any rational number, and you'll be able
to find a geometrical configuration producing it somehow.
interesting...
danny