Around 255 BC Eratosthenes was working in the library of Alexandria. While studying and ordered the papyrus called his attention to a report on some interesting observations in Siena (now Aswan, Egypt) southeast of Alexandria. According to the report, in Siena, in the summer solstice objects cast no shade and the sun can be reflected in the bottom of the wells. (This means that the city is located just above the line of latitude tropics and is therefore equal to that of the ecliptic, Eratosthenes data already knew). Eratosthenes reasoned that if Siena and Alexandria were the same length (distance only 3 ยบ), the same experiment under identical conditions but in Alexandria, should give the same results. Observations made in Alexandria, the summer solstice day, same time as those described in the report of Siena. First measured the height of a tower and the length of its shadow at noon on June 21 in Alexandria. Then calculated the angle formed by the sun's rays to the vertical, this angle matches the circumference subtended by the arc connecting the cities of Siena and Alexandria.
Eratosthenes correctly assumed that if the sun was at a great distance, its rays reaching the earth, parallel and should reach, if it was flat as was thought in those days, you should not find differences between the shadows cast by objects at the same time of day, regardless of where they met. However, found substantial discrepancies between the results measured in Siena and Alexandria, so he deduced that the land could not be flat.
then took the distance estimated by the trade caravans between cities fixing in 5000 stadia (Greek unit of length), so the angle measured from the shadows, he calculated the circumference of the earth in about 252,000 stadia.
Admitting that Eratosthenes used the stage of 185 m, the error was 6,616 km (about 17%). But others argue that the stadium used Egyptian (300 cubits of 52.4 cm), in which case it would have been calculated the circumference of 39614.4 km, which compared with 40,008 km currently considered, has a lower error 1%.
We must consider the difficulty of this experiment, since Eratosthenes should not only accurately measure the height of a building, but also the shadow and it, at its upper end is not clear.
In the summer solstice solar rays perpendicularly Siena (1). Alexandria (2), further north, if we measure the height of a building and the length of the shadow cast, you can determine the angle with the plane of the ecliptic, which include the Sun City Siena. This angle is precisely the difference of latitude between the two cities. Known it is sufficient to measure the arc of a circle and extrapolate the result to the complete circle (360 degrees).
hundred and fifty years later, Posidonius performed again the calculation of Eratosthenes obtained a circumference substantially retail value adopt Ptolemy and Columbus would be based to justify the feasibility of travel to the West Indies.
Despite the overwhelming demonstration of Eratosthenes did not allow the roundness of the Earth until much later ...
Bibliographical Notes:
Eratosthenes was born in Cyrene (Libya) in 276 a. C. and studied in Alexandria and Athens. He was an astronomer, historian, geographer, philosopher, poet, theater critic and mathematician. Around the year 255 BC was the third director of the Library of Alexandria where he was intensively and made his great contribution to science and astronomy to determine the size and shape of the earth. We must also create the armillary sphere (Astrolabe). the end of his life, affected by blindness, starved of their own volition in 194 BC in Alexandria.
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