Can you measure the Earth with a stick?

That time, that place

Eratosthenes ran the Library of Alexandria. He did mathematics, geography, and poetry, and the story goes that because he was not first in any one of them, people called him Beta — number two.

Why this question

In the southern city of Syene there was a curious well: only at noon on the summer solstice did sunlight reach its bottom, meaning the Sun stood exactly overhead.

Yet on that same day at that same hour, a rod set up in Alexandria cast a shadow. If the ground were flat the shadows would match. That they differ means the surface between the two cities curves.

What was found

The shadow's angle came to about 7.2 degrees — one fiftieth of a full circle. So multiply the distance between the two cities by fifty and you have the way around the Earth.

He estimated that distance from how many days the caravans took. The figure he arrived at differs from today's value by only a few percent. What it required was a rod, a shadow, and a proportion.