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?
In: Mathematics
If you take a stick and pop it on the ground, the length of its shadow will change as the sun moves overhead.
The point where the shadow is shortest is noon (the sun is the most overhead).
So, as the shadow moves just trace its path on the ground.
Do this in your two locations, and take the shortest lengths from both, and you have your two ‘noon’ measurements.
If you’re at the equator and the sun is directly overhead, the shadow length will shrink down to essentially zero. But further away from the equator, the sun will be ‘off-center’ and so it will always have some positive length. This distinction is what Eratosthenes noticed, and the basis for the calculation itself.
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