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How Eratosthenes of Cyrene Proved the Earth was round 2000 years ago


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Collecting Information

Eratosthenes was a librarian, poet, mathematician, and astronomer.  He was born in a Greek colony called Cyrene—located in modern day Libya—in 276 BC.  When he was 40 years old, he became the chief librarian of the Library of Alexandria, an enormous repository of information from a myriad of locations and intellects.  He continued collecting information throughout his lifetime and eventually contributed some findings of his own.

Developing Latitude and Longitude

Eratosthenes is credited with inventing the field of geography and developed the first system of latitude and longitude for plotting precise locations on Earth. In his system it was possible to estimate the distance from any known points on Earth at the time. He also calculated the angle of Earth’s tilt and documented a catalog of 675 stars. 

Sieve of Erathosthenes

His “sieve,” known today in math classrooms as the Sieve of Eratosthenes is a method to quickly and efficiently find prime numbers.  In the sieve, a list of consecutive integers is generated starting with two and ending with any number (n). After two, every second number of the list is crossed out (even numbers). Since the next number is three, every third number is crossed out in the next step. Four is crossed out, but five is next, so every fifth number is crossed out. As the pattern continues, composite (non-prime) numbers are crossed out and prime numbers such as 5, 7, 9, 11, 13, 17, and onward are left behind. 

Circumference of the Earth

Eratosthenes’ most important contribution, however, may have been his calculation of Earth’s circumference using geometry and trigonometry.  Eratosthenes noticed that at noon on the summer solstice in an Egyptian well, the sun’s rays shone directly into the well and lit up the water—meaning that at that day and time, the sun was right above the well.  He then put up a tall pole in Alexandria that cast a shadow on the summer solstice, meaning that the sun was positioned slightly south from the pole.  After measuring the distance between the well and the pole and taking into account the Earth’s spherical nature, Eratosthenes measured the angle of the sun’s rays on the day of the solstice and related that in a proportion to the circumference of the Earth.  His calculation, while not totally airtight, yielded a high degree of accuracy. The same calculations performed today, with accurate data, result in the circumference of the Earth measuring only 66 kilometers off from its actual, accepted circumference. 

Eratosthenes died at the age of 82.  Although most of his original writings have been lost to history, we do have evidence of his mathematical work and astronomical findings which are highly relevant in both fields today.

 

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