# ERASTOTHENES -FOUNDER OF MATHEMATICAL GEOGRAPHY

Erastosthenes, son of Agloas, was born in Cyrene but spent most of his life working in Alexandria, where he was head of the library attached to the famous Museum from ca, 235 until his death. Eratosthenes was one of the notable scholars of his time and produced works on geography, mathematics, philosophy, chronology, literary criticism, and grammar as well as writing poetry. His most lasting work was in geography, the most notable his measurement of the circumference of the earth. This work was on of the first attempts to put geographical studies on a proven mathematical basis. Therefore, he has been called the founder of mathematical geography.

### Eratosthenes' calculation of the earth's circumference

Eratosthenes assumed that the city of syene was on the Tropic of Cancer because at midday on the summer solstice a well, especially dug for this reason, was illuminated to its bottom by the sun's rays. It was also assumed that the city of Alexandria and Syene were on the same meridian. On the next solstice, Eratosthenes measured the shadow cast at Alexandria at midday by a vertical pointer (thin stylus) of known height. The vertical angle of this shadow was found to be 82 degrees 48 minutes. North Pole Tropic of Cancer Alexandria rays of sun Equator Syene Since the angle of the sun's rays on the summer solstice is 90 degrees, then both vertical lines extended to the center of the earth would form an angle of 7 degrees 12 minutes ( all three angles totaling 180 degrees). Therefore, the arc distance between Syene and Alexandria relative to the earth's circumference would be 7 degrees 12 minutes/360 degrees, or 1/50 of the circumference.

Eratosthenes assumed the distance between the two cities at 5,000 stadia (575 miles). Since this distance was 1/50 of the whole circle, the total circumference was determined to be 250,000 stadia (5,000 stadia X 50), or 28,750 miles.

The method used by Eratosthenes was sound in theory, but his data and assumptions were inaccurate. Although the figure of 1/50 of the circle for the difference in lattitude is correct, Syene is not directly on the Tropic of Cancer. Alexandria does not lie on the same meridian (it lies some 3 degrees to the west). And the distance between the two cities is closer to 4,530 stadia, not 5,000. Eratosthenes was aware that the distance between the two cities was doubtful, so to compensate for the error he added 2,00 stadia to the final result.

Despite these inaccuracies, the whole measurement was a very valuable achievement and was not bettered until modern times. Eratosthenes' final calculation of the circumference of the earth was only 15 percent larger than the modern figure of a little less than 25,000 miles.