Eratosthenes’ Calculation of Earth’s Circumference

The first person to measure the size of the earth was Eratosthenes, an ancient Greek scientist, about 2,000 years ago.

Eratosthenes lived in the city of Alexandria, near the mouth of the Nile River by the Mediterranean coast, in northern Egypt. He knew that on a certain day each year, the Summer Solstice, in the town of Syene in southern Egypt, there was no shadow at the bottom of a well. He realized that he could determine how far away from directly overhead the Sun was in Alexandria by measuring the angle formed by a shadow from a vertical object.

He measured the length of the shadow of a tall tower in Alexandria, and used simple geometry to calculate the angle between the shadow and the vertical tower. This angle turned out to be about 7.2 degrees. Next, Eratosthenes used a bit more geometry to reason that the shadow’s angle would be the same as the angle between Alexandria and Syene as measured from the Earth’s center. And he found that the distance from Alexandria to Syene is about 925 km. Therefore, assuming that the earth is perfectly spherical, he used the principle that the center angle and the length of the arc are proportional to each other in the circle.

He calculated the circumference of the earth at about 46,000 km. This value is slightly larger than today’s measured value of about 40,075 km, but it is very accurate with the measurement technology at that time.

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