Calculatory Notes

I drew up a small mock-up of Eratosthenes' diagram of how he reasoned the size of the earth's circumference.

Point C is the center of the planet; point A is in Alexandria, and the line CA is the extension of the post in Alexandria; point B is Syene, and the line CB is that respective extension; line PA is a line parallel to CB, and represents the shadow cast by the post in Alexandria (remember there was no shadow cast in Syene).



The angle created by PAC is the same angle created by ACB by the equivalency of opposite interior angles axiom from Euclidean geometry. Eratosthenes calculated it at seven degrees.

Now, I'll be the first to state that the universe isn't Euclidean, but rather non-Euclidean hyperbolic space (on the scale of the very large, anyway), but hyperbolic space under Einstein's general relativity equations break down to basic Euclidean constructions and laws on the global, or "small" scale.

I apologize for the crudeness of the sketch, math-people.