system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Eristothenes measured the circumference of the earth by measuring the shadow of two poles, miles apart, at the exact same time. So how did he know the poles were being measured at exactly the same time in an era when people used the sun for timekeeping?
gpt
By doing it at local apparent noon. This is, by definition, the time of day when the sun reaches its highest point in the sky. If 2 places are on the exact same line of longitude (i.e., directly north and south of each other), local apparent noon will occur at exactly the same time in both places. You can, of course, measure this with a sundial.

It turns out that while close, Alexandria and Syene (modern day Aswan) are not directly north and south of each other, which introduced some error into his calculations. Still, they're close enough that his measurement was remarkably close to the correct value.