Eratosthenes - Measuring the Circumference of the Earth in 240 BC


Eratosthenes was a Greek scientific writer, astronomer, and poet, who is credited with making the first approximation of the size of the Earth for which any details are know. He was born in Cyrene, Libya c. 276 BC. After studying in Alexandria and Athens, he settled in Alexandria around 255 BC and became director of the Great Library there.

In the town of Syene (now Aswan) in Egypt, it was well known that at noon on the day of the Summer solstice, light from the sun would shine directly down a local well. One could look down the well and see his or her own shadow at the bottom, but no shadow from the sides of the well. Eratosthenes found it curious that this never happened at any day in Alexandria. And so he was acutely aware that there was something to be learned from this phenomenon. He began to observe the distance of a shadow caused by a very tall tower in Alexandra. He noted that in Alexandria at the same time, during the same day, sunlight fell at an angle of about 7.2 degrees from the vertical. Eratosthenes records this angle to be "a fiftieth of a circle", as measuring angles in degrees had not yet been adopted from the Babylonians at this point.

He correctly assumed the sun's distance from the Earth to be very great, and therefore rays of light falling towards the Earth to be parallel. If he could determine the distance from Syene to Alexandria, all he would have to do to determine the circumference of the Earth was multiply this distance by 50. And so he enlisted the talents of a professional pacer to determine the exact distance from the well in Syene to the tower in Alexandria. He determined that Alexandria is about 5,000 stadia (489 miles) North of Syene.

Eratosthenes parallel sun rays used determine the circumference of the Earth

Given these estimations, Eratosthenes was able to calculate the circumference of the Earth to be 250,000 stadia. The length of one stadia is not exactly known, but it is thought to be between 515 and 686 feet. This corresponds to a circumference of between 24,384 and 32,481 miles, but it is likely that he calculated a value of about 25,000 miles. Compared to today's accepted measurement of the Earth's circumference of 24,901 miles, Eratosthenes' calculation is off by less than 1%.

Calculating the circumference of the Earth to within 100 miles is remarkably accurate given that it was done around 240 BC. Had Christopher Columbus used these measurements for the Earth's size, he might have realized that he had discovered a new continent in 1492, instead of believing he had arrived in India. Eratosthenes also measured tilt of the Earth's axis, and wrote at length of the eight year lunar-solar cycle. He is remembered by history as a great contributor to the field of astronomy. He would die in Alexandria in c. 194 BC at the age of 82.

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  The Britannica Guide to Geometry

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