Measuring Earth with a Stick

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Measuring Earth with a Stick
Have you ever heard of the Greek mathematician and astronomer Eratosthenes? His name is probably best known among astronomers. Why do they think so highly of him?
Eratosthenes was born about 276 B.C.E. and received some of his education in Athens, Greece. He spent a good part of his life, however, in Alexandria, Egypt, which at that time was under Greek rule. In about 200 B.C.E., Eratosthenes set out to determine the dimensions of the earth by using a simple stick. “Impossible!” you may say. How did he do it?

In the city of Syene (now called Aswan), Eratosthenes observed that at noon on the first day of summer, the sun was directly overhead. He knew this because there was no shadow cast when the sunlight reached the bottom wells. However, at noon on the same day in the city of Alexandria, which was located 5,000 stadia (stadia were Greek units of length. Through the exact value varied locally, one stadium is believed to have been 530 to 600 feet) to the north of Syene, a shadow could be observed. That gave Eratosthenes an idea.

Eratosthenes set up a gnomon, a simple upright stick. When the sun was overhead at noon, he measured the angle of the shadow that the stick cast in Alexandria. He determined the angle to be 7.2 degrees from vertical.

Now, Eratosthenes believed the earth to be spherical, and he knew that there are 360 degrees in a circle. So he divided 360 by the angle he had measured, 7.2. The result? His angle was one fiftieth of a full circle. He then deduced that the distance from His angle was one fiftieth of a full circle. He then deduced that the distance from Syene to Alexandria, or 5,000 stadia, must be equal to one fiftieth of the circumference of the earth. By multiplying 50 by 5,000, Eratosthenes came up with 250,000 stadia as the circumference of the earth.

How close did his figure come to present-day calculations? The figure of 250,000 stadia is equal to between 25,000 and 29,000 miles...
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