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You can do this whole thing on a calculator.
At noon on the longest day, a stick in Syene cast no shadow, and a stick in Alexandria did. The angle of that shadow was a fiftieth of a circle. In
degrees, 360 divided by 50 is 7.2.
Because sunlight comes in parallel, that shadow angle is the same as the angle at the center of the Earth between the two cities. So the trip from Alexandria to Syene is a fiftieth of the way around the planet.
Check it: 360 divided by 7.2 is 50.
The cities were 5,000 stadia apart. 5,000 times 50 is 250,000 stadia around the whole Earth.
A stadion was about 157 metres (157.7 by the best Egyptian estimate). 250,000 times 157.7 metres is 39,425 km, about 39,400 km. The real distance around the Earth through the poles is 40,008 km. He was off by about 1.5%
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2026/11/05
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