Assignment #1 - Eratosthenes

Eratosthenes was born in Cyrene, Greece (which is now in the country of Libya) in about 276 B.C.E. Although he was best known as a Greek mathematician, in addition, he was also a scientist, poet, astronomer, and geographer. Eratosthenes studied philosophy and mathematics in Athens when he was younger. As time passed his research became known and Eratosthenes began to make a name for himself, Ptolemy III especially noticed this and called him to Alexandria, Egypt for two main reasons. The first reason was to tutor his son and the second was to be the librarian for the Library of Alexandria. 

This library contained almost a million books in the form of scrolls, lecture rooms, and meeting halls and would be classified today as a university. Eratosthenes is said to have committed suicide by voluntary starvation in 255 B.C.E. Though little remains of his original work, Eratosthenes is credited with two major discoveries: the measurement of the size of the Earth and his sieve for finding prime numbers.

 

Prime numbers are numbers that can only be divisible wholly by itself and by 1. Eratosthenes’ sieve is still used today in mathematical research to find prime numbers. He discovered that if all natural numbers were written down from 2 to infinity and every other number after 2 was removed, then the multiples of 3 were then removed, and it was continued with the next available number and so on, it would leave a list of prime numbers. This could then be used to find primes for any limit needed.

During the longest day of the year, Eratosthenes noticed there were no shadows upon the walls of Syene, a city just south of Alexandria, due to the Sun being directly above the city at this time of day. Since he noticed that there were shadows in Alexandria, which was just north of Syene, he figured that there was a correlation with the angle of the shadows and the circumference of the Earth. He did this under the assumption that the Sun was so far away that its rays were parallel and that the Earth was a sphere. Eratosthenes then used his knowledge of the angles of the rays/shadows falling on Alexandria and Syene along with the distance between the two cities to calculate the circumference of the Earth.

Eratosthenes calculated the Earth’s circumference as approximately 250,000 stadia, which is converted to approximately 25,000 miles (~40,233.6 km). Currently, the circumference of the Earth is known as 40,075 km meaning that his approximation back then is within 1% accuracy to the actual value of the circumference of the Earth. His findings were a huge advance in a time where the Earth was not perceived as a spherical object.