Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that at local noon on the summer solstice in the Ancient Egyptian city of Swenet (known in ancient Greek as Syene, and now as Aswan) on the Tropic of Cancer, the Sun would appear at the zenith, directly overhead. He knew this because he had been told that the shadow of someone looking down a deep well in Syene would block the reflection of the Sun at noon off the water at the bottom of the well. Using a gnomon, he measured the Sun's angle of elevation at noon on the solstice in Alexandria, and found it to be 1/50th of a circle (7°12') south of the zenith. He may have used a compass to measure the angle of the shadow cast by the Sun.[16] Assuming that the Earth was spherical (360°), and that Alexandria was due north of Syene, he concluded that the meridian arc distance from Alexandria to Syene must therefore be 1/50th of a circle's circumference, or 7°12'/360°.
His knowledge of the size of Egypt was founded on the work of many generations of surveying trips. Pharaonic bookkeepers gave a distance between Swenet and Alexandria of 5,000 stadia. Some say this distance was corroborated by inquiring about the time that it took to travel from Syene to Alexandria by camel. Carl Sagan says that Eratosthenes paid a man to walk and measure the distance. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. Some claim Erathostenes used the Egyptian stade of 157.5 meters, which would imply a circumference of 39,690 km, an error of 1.6%, but the 185 meter Attic stade is the most commonly accepted value for the length of the stade used by Eratosthenes in his measurements of the Earth,[17] which imply a circumference of 46,620 km, an error of 16.3%. It is unlikely, however, that Eratosthenes got an accurate measurement of the circumference of the Earth, given three errors in the assumptions he made:[16]
That Alexandria and Syene lie on the same meridian. That the distance between Alexandria and Syene is 5000 stades.
That the Earth is a sphere.
If we repeat Eratosthenes' calculation with more accurate data, the result is 40,074 km, which is 66 km different (0.16%) from the currently accepted circumference of the Earth.[16]
Seventeen hundred years after Eratosthenes' death, while Christopher Columbus studied what Eratosthenes had written about the size of the Earth, he chose to believe that the Earth's circumference was much smaller. Had Columbus set sail knowing that Eratosthenes' larger circumference value was more accurate, he would have known that the place where he made landfall was not Asia, but rather a New World.[18]
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