Eratosthenes's Measure of the Earth's Circumference
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Eratosthenes measured the circumference of Earth around 240 BC, based on the fact that the Sun appears in the zenith at noon on the summer solstice, in Syene (modern Aswan). At the same time, in Alexandria, the angle of the shadow of a post was slightly more than 7° (you can vary this parameter in this Demonstration), which is roughly 1/50 of the circumference (7/360 ≈ 0.0194444); the distance between the cities is 5000 stadia (an ancient Greek unit, about 185 meters) or about 925 km. The calculation gives 925/.02 ≈ 46250 km, a value very near today's value of 40000 km, with an error of 16%; an amazing feat for the epoch in which he lived.
Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA
Reference: Eratostheneson Wikipedia.
"Eratosthenes's Measure of the Earth's Circumference"
Wolfram Demonstrations Project
Published: March 7 2011