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Measurement Session 5: Notes
 
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Note 10

This problem has a great deal of history behind it. Eratosthenes is credited with using this approach to calculate the circumference of the Earth. He concluded that the only explanation for why no shadows fell at Syene at midday on June 21 but did fall at Alexandria was because of the curvature of the Earth. He then devised a method for finding the circumference of the Earth that is based on constant-ratio calculations involving proportions. On the day of the summer solstice, he measured the direction of the Sun's rays as they struck an obelisk in Alexandria and an angle between them. This angle (we'll call it A) can be compared to 360 degrees, and this ratio can in turn be used in the following proportion:

He measured A to be 8 degrees and the distance from Alexandria to Syene as 4,800 Greek stadia (a stadia corresponds to approximately 606.75 ft.). He then set up a proportion similar to the one above. Eratosthenes's approximate measurement for the circumference of the Earth was very close to today's modern value.

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