Eratosthenes

     The accomplishment that Eratosthenes is probably most well known for was his estimation of the circumference of the Earth. Although not many believed it at the time, Eratosthenes knew that the world was round which allowed him to make this discovery. He knew from observation that in the town of Syene in Egypt, the sun shone straight down the wells because of the way the sun reflected. He realized that because of the huge distance between the sun and the earth, all light waves must be parallel. Because the earth was curved, the light would hit a different city at a different angle. Eratosthenes went to Alexandria and found out that the light hit the earth at an angle of 7.2 degrees. This meant that if he continued the light waves at Alexandria and the light waves at Syene, they would meet at a 7.2 degree angle at the center of the earth. Since 7.2 degrees is one fiftieth of a circle (360 degrees), the distance between Alexandria and Syene would be one fiftieth of the circumference of the earth. He measured this distance as approximately 5000 stadia, a measurement equal to about 500 miles or 800 kilometers. When he multiplied this distance, he got about 250,000 stadia, equal to 25,000 miles or 40,000 kilometers. The actual  circumference around the equator is about 24,900 miles, which means that Eratosthenes was incredibly accurate in his estimation.
Note: There is much debate among scientists and historians of today about the length of a stadia, because with some proposed lengths Eratosthenes would have been off in his measurement by more than 100 miles. However, in any case it is a remarkable estimate for someone to have made during the time period.

     Another main accomplishment of Eratosthenes was creating an algorithm for discovering prime numbers. This algorithm is called the sieve of Eratosthenes. The sieve of Eratosthenes works by eliminating all the numbers up to a certain number that are not prime. The first step in the algorithm is to list all the numbers from 2 to the n, the number up to which all prime numbers will be found. The first number, 2, is called p and is the first prime. The next step is to eliminate all the multiples of p (in this case 2) that are greater than the number itself. Once this is done, the next number that remains after 2 is the new p. All the multiples of p are again eliminated, and this process of eliminating the multiples of the next number is continued until p becomes greater than the square root of n. At this point all the numbers that remain are prime.

http://en.wikipedia.org/wiki/File:New_Animation_Sieve_of_Eratosthenes.gif
http://nlvm.usu.edu/en/NAV/frames_asid_158_g_3_t_1.html - set n, then click on the number p to eliminate the non primes

     Eratosthenes also did other things that are known today. He made maps, both of the world and sky and is said to have made a map that included 675 stars. He worked in geography to try to figure out why the Nile river had such a regular flood pattern, and hypothesized that it was because of heavy rain upstream. He estimated the distance to the moon and the distance to the sun from earth, although neither one of these estimations is thought to be particularly accurate. In astronomy he also calculated the angle that the earth's axis is tilted on. In mathematics, Eratosthenes discussed doubling a cube and is thought to have worked to find a solution. Eratosthenes created a calendar with leap years, and he also worked as a historian to give dates for past events in Greek history.