ERATOSTHENES OF CYRENE

Eratosthenes was born in Cyrene, now in Libya, and educated at Athens. He then taught in Alexandria where he became tutor to the son of Ptolemy III and librarian. He was prominent in history, poetry, mathematics, and astronomy and was known by the nickname ‘beta’ because, some say, he was the second Plato.

In number theory he introduced the procedure named for him to collect the prime numbers by filtering out all the composites. The method, called the sieve of Eratosthenes, was to write down a list of ordered numbers and to strike out every second number after 2, every third number after 3, every fourth number after 4, and so on. The numbers remaining are primes.

Eratosthenes achieved his greatest fame by using a most ingenious and simple method to measure the circumference of the Earth. He was aware that on a certain day the Sun at Syene (now Aswan) was exactly at its zenith (it was known to shine directly down a deep well on that day). He found that on the same day at Alexandria it was south of its zenith by an angle corresponding to 1/50 of a circle (7° 12'). He also knew that the distance between Syene and Alexandria was 5000 stadia – a distance that he estimated from the time it took a camel train to make the journey. Therefore, 5000 stadia must be 1/50 of the circumference of the Earth; that is, 250,000 stadia. (Since the exact length of a stade is not known it is impossible to work out exactly how accurate his measurement was but it has been thought to be within 50 miles of the presently accepted value.) Eratosthenes also established an improved figure for the obliquity of the ecliptic (the tilt of the Earth's axis) of 23°51'20''. Finally, he produced the first map of the world, as he knew it, based on meridians of longitude and parallels of latitude.