# Eratosthenes

Updated on June 20, 2010

Eratosthenes was born in Cyrene on the North African coast of the Mediterranean Sea (in present day Libya) in about 276 BC. His teachers included the philosopher Ariston, a former pupil of the mathematician Zeno. Eratosthenes studied for a number of years at Athens before moving to Alexandria at the invitation of Ptolemy III of Egypt to be its librarian and to be a tutor for Ptolemy’s son.

Eratosthenes was very gifted. Not only was he a mathematician, but he was also an astronomer, an historian, a geographer, and even an athlete. His prowess in athletics earned him the nickname Pentathlus , which means ‘Champion in 5 athletic sports’. He was also a poet. His poem, named Hermes , records the fundamentals of astronomy in verse.

Eratosthenes provided a mechanical solution of the problem known as ‘The duplication of the cube’ i.e. constructing a cube of volume exactly twice that of a given cube. However, he is probably best known for his famous sieve – The Sieve of Eratosthenes (see below).

Eratosthenes is also famous for his determination of the circumference of the earth. This was recorded in his treatise named On the Measurement of the Earth , the original of which has unfortunately been lost. It is believed that Eratosthenes made his estimate by using similar triangles, together with knowledge of the angle of elevation of the sun at noon on the summer solstice, and known distances between towns. Using these facts he was able to estimate the circumference of the earth to be about 24,500 miles, which is remarkably close to the actual value of 24,860 miles. It may be coincidence that his estimate is so good, but it does demonstrate his genius. But what also makes his method remarkable is that he knew that the Earth is a sphere and not a flat disc as some believed.

In his old age Eratosthenes became blind, and he died at the age of more than eighty years in about 195 BC.

## A contribution of Eratosthenes to mathematics

Eratosthenes is said to be the discoverer of ‘The Sieve of Eratosthenes’, a method to find all prime numbers less than any given number. To illustrate the method, I will find all the prime numbers less than 100:

The Sieve of Eratosthenes shows that the prime numbers less than 100 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97

2

24

26

31

10

10