The great mathematician Eratosthenes was born in Cyrene, North Africa (now Shahhat, Libya), in about 285 B.C. (O"Conner 1) He would go on to live in Athens, Greece and then Alexandria, where he was named Librarian of the Royal Library of Alexandria; he would eventually become known as "The Great Alexandrian Scholar" (Fraser 4) and the "Pentathlete" (Mahoney 542).
One of Eratosthenes" most famous works was the Platonicus, which dealt with the mathematics underlying Plato's philosophies. The book is now lost forever, but records show that it dealt with such topics as the basic definitions of geometry and arithmetic, as well as covering music. (O"Conner 1) The most important of Eratosthenes" findings is his ingenious measurement of the earth's circumference; he was able to measure the angle between the sun's rays and a perpendicular line at the same time in Alexandria (Mahoney 541).
Eratosthenes also worked on prime numbers, and is remembered for his prime number sieve, the "Sieve of Eratosthenes," which, in modified form, is still an important tool in number theory research (O"Conner 2). It ultimately eliminates all multiples of the successive prime numbers beginning with 2 (Mahoney 543). The sieve can help solve math problems such as this one: "What are all the prime numbers up to 100?" (Stanton 13). Using the sieve, we can write down all the integers from 2-100 in columns following a certain pattern. We start with 2 and then cross out every second number after it up to 100; then, we circle 3 and then cross out every third number after it and so on. In the end, all the circled numbers will reveal all the prime numbers of 100. (Stanton 14).
Eratosthenes also made a surprisingly accurate measurement of the Earth's circumference, detailed in his treatises, On the Measurement of the Earth, which is also lost. He assumed that the sun was so far away that its rays were essentially parallel, and then with a knowledge of the distance between Syene and Alexandria, he gave the length of the circumference of the Earth as 250,000 stadia.
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