# Eratosthenes

Eratosthenes of Cyrene was a Greek mathematician who lived from about 275-195 B.C. Today he is best known for his contributions to geography, mathematics, and astronomy. Educated in Athens, Greece, and in Alexandria, Egypt, Eratosthenes was appointed director of the great Library at Alexandria in 236 B.C., where he served for several years.

One famous contribution that bears his name, the "Sieve of Eratosthenes," is a system for finding prime numbers. However, Eratosthenes' most famous accomplishment is his calculation of the circumference of the Earth to a remarkable degree of accuracy for his time.

In determining the circumference of the Earth, he had read that a certain deep well near Syene, a city due south of Alexandria, was fully illuminated by the sun at noon on the summer solstice. The sun, therefore, must have been directly over the well. Seeing that a pole in neighboring Alexandria cast a shadow at the same time, Eratosthenes measured the angle of that shadow and used it to calculate the curve of the Earth. He assumed two things in his calculations: that the Earth is round and that the Sun is far enough away that its rays are essentially parallel. He then used a primitive version of the arc length formula to calculate X, the circumference of the Earth, in the proportion: X/x = Y/y

In this formula, x equals the distance between Syene and Alexandria; Y equals the 360 degree angle of the round Earth; and y equals the angle of the shadow cast at Alexandria.

Eratosthenes also successfully measured the tilt of the Earth's axis, created a catalogue of 675 stars, and wrote mathematical and geographical treatises, all of which are now lost to us. One was titled Platonicus, which dealt with the mathematics behind Plato's philosophy. We do know that he also devised a map of the known world, divided by a system of longitude and latitude.

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