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| Eratosthenes made a remarkably precise measurement of the size of the Earth. He knew that at the summer solstice (solen passerer vendekretsen; 21. september) the sun shone directly into a well at Syene at noon. He found that at the same time, in Alexandria, Egypt, approximately 787 km due north of Syene (now Aswan), the angle of inclination of the sun's rays was about 7.2°. With these measurements he computed the diameter and circumference of the Earth. |
How did Eratosthenes get a result?
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Since light rays travel parallel to each other, we get pairs of congruent
angles. With the central angle measuring 7.2° and the length of the
arc between Syene and Alexandria 787 km we can write the proportion:
7.2 787 ---- = ---- 360 X therefore X = 39350 km, the circumference. From this, one finds the radius R = 6263 km via the formula X = 2 Pi R |
Who was Eratosthenes?
The Search for Primes