LYCOS RETRIEVER 
Eratosthenes: Distances
built 255 days ago
Eratosthenes' method for determining the size of the Earth was an elegant application of simple geometry to an otherwise very difficult problem. By using the difference in the elevation of the noontime sun at two different locations, he was able to measure the angular difference betwen the vertical directions at those two locations. This angular difference told him what fraction of the way around the earth separated the two locations. He then used this fraction and the measured distance between the two locations to estimate the distance around the earth (a.k.a. the circumference).
Source:
Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as, Syene) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He ... knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 1/50 of a full circle (7°12') south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. His estimated distance between the cities was 5000 stadia (about 500 geographical or nautical miles). He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued.
Source:
Eratosthenes investigated arithmetical and geometrical problems. In his "sieve" method of distinguishing prime numbers, by which "the prime and incomposite numbers are separated by themselves as though by some instrument or sieve," there is the foundation for a logical theory of the infinite. The prime numbers were found by listing all odd numbers beginning with 3, then striking out every third number, every fifth number, and so on, with the remaining numbers being the primes. The much-attempted problem of the duplication of the cube, which dealt with the problem of finding the mean proportional between two lines, occupied Eratosthenes at an early date. To solve it, he constructed a bronze instrument called a mesolabe. He ... applied geometrical methods, by ascertaining both the difference of latitude and the distance apart of two places that were supposedly located on the same meridian, to deduce the circumference of the earth.
Source:
Eratosthenes used the lengths of shadows to figure out how high in the sky the Sun was in a certain place on a certain day. He knew of another place where there was no shadow at all on the same day. That meant the Sun was straight overhead. He found out the distance between the two places, then used some geometry to figure out the rest. Let's take a closer look!
Source:
According to the Greek historian Cleomedes, Eratosthenes measured the angle between the sunlight and the stick at midday in midsummer in Alexandria to be 7.2 degrees, or one-fiftieth of a complete circle. It is evident on drawing a picture of this that this is the same angle as that between Alexandria and Syene as seen from the center of the earth, so the distance between them, the 5,000 stades, must be one-fiftieth of the distance around the earth, which is therefore equal to 250,000 stades, about 23,300 miles. The correct answer is about 25,000 miles, and in fact Eratosthenes may have been closer than we have stated here---we’re not quite sure how far a stade was, and some scholars claim it was about 520 feet, which would put him even closer.
Although Eratosthenes' method was well founded, the accuracy of his calculation was inherently limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is not precisely on the Tropic of Cancer, is not directly south of Alexandria, and the Sun appears as a disk located at a finite distance from the Earth instead of as a point source of light at an infinite distance. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity, overland distance measurements were not reliable, especially for travel along the non-linear Nile which was traveled primarily by boat. So the accuracy of Eratosthenes' size of the earth is surprising.
Source:
MORE ABOUT
Distances