# How Did the Greeks Figure Out the Size of the Earth?

The Greek Eratosthenes, who lived around 250 B.C., was the first man we know of to figure out the size of the earth. Yet he never traveled around the earth, nor did he have any of today’s measuring equipment. How, then, did he do it?

Eratosthenes used Euclid’s principles of geometry to solve the problem. First he learned that at noon on the longest day of the year, the sun shone straight down to the bottom of a well in the Egyptian city of Syene.

At the same time, in the city of Alexandria, the sun caused an upright post to cast on the ground a shadow shaped like a right triangle, a triangle with one 90° angle. Eratosthenes then measured the other angles and found that one angle was equal to 1/50 of an entire circle.

He then determined that if the lines formed by the post at Syene and the well at Alexandria were extended downward, they would form two sides of another right triangle at the center of the earth. Again using geometry, Eratosthenes proved that one angle of the second triangle was equal to one angle of the first triangle or 1/50 of an entire circle.

Since the earth’s circumference between Syene and Alexandria formed an arc, that arc was also equal to 1/50 of the earth’s circumference. Eratosthenes knew that the distance between Syene and Alexandria was 5,000 stadia (a Greek measure), so he then multiplied it by 50, and found that the distance around the earth was 250,000 stadia, or 24,670 miles.

How close was Eratosthenes back in 250 B.C.? The circumference of the earth is now known to be 24,900 miles! Quite a feat for a time so long ago!