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Around 240 BCE, Eratosthenes used shadows to estimate Earth’s size. At Syene, the Sun was straight overhead, but in Alexandria, a stick made a shadow. Using that angle, the city distance, and geometry, he calculated Earth’s circumference surprisingly close to the modern value.

Here’s how he did it:

In Syene, at noon on a certain day, the Sun was almost straight overhead. A deep well had sunlight at the bottom, and a vertical stick made almost no shadow.

On the same day and time in Alexandria, a vertical stick did make a shadow.

He measured that shadow and found the Sun’s angle there was about 7.2 degrees.

A full circle is 360 degrees.

7.2 degrees is 1/50 of 360.

That meant the distance from Syene to Alexandria was about 1/50 of Earth’s full circle.

So he took the distance between the two cities and multiplied it by 50.

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