1. The problem statement, all variables and given/known data The Shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 the Earth's radius. Is there a geometric connection between these two 1-to-8 ratios? 2. Relevant equations Not sure exactly what kind of answer they are looking for here.
Welcome to PF! Hi NateTheGreat! Welcome to PF! You've left out that at noon during the summer solstice, the sun at Syene is directly overhead. (I know that 'cos this is a well-known experiment by Eratosthenes in about 200 BC ) Does that help?
Re: Welcome to PF! Ah! So then would that explain why they are both 1/8 of the Earth's radius? I'm trying to figure out what they mean by a "geometric connection"?
Look at this flashy simulation of the experiment, it is a demo but you can see from it the basic geometry used. Here