Eratosthenes of Cyrene (275-194 B.C.)
Eratosthenes of Cyrene (275-194 B.C.) scientific writer, astronomer, geographer and poet, he was the first Greek mathematician to calculate the circumference of the earth and the tilting of the earth's axis during rotation. He used principles of Euclidean geometry.
He also invented the sieve of Eratosthenes, which is a technique for separating composite from prime numbers in a natural series. The sieve appears in the Introduction to arithmetic by Nicomedes.
Eratosthenes was the third librarian at Alexandria; in addition to his knowledge in many different areas, he was an accomplished mapmaker. Eratosthenes also made a catalogue of stars with 675 stars listed in it. His followers called him the second Plato.
He was, indeed, recognized by his contemporaries as a man of great distinction in all branches of knowledge, though in each subject he just fell short of the highest place. On the latter ground he was called Beta, and another nickname applied to him, Pentathlos, has the same implication, representing as it does an all-round athlete who was not the first runner or wrestler but took the second prize in these contests as well as others. Eratosthenes died in 194 BC in Alexandria, Egypt. (Oxford, 1921)
Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead (he had been told that the shadow of someone looking down a deep well would block the reflection of the Sun at noon). He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun was 1/50th of a circle (7°12') south of the zenith on the solstice noon. Assuming that the Earth was spherical (360°), and that Alexandria was due north of Syene, he concluded that the meridian arc distance from Alexandria to Syene must therefore be 1/50 = 7°12'/360°, and was therefore 1/50 of the total circumference of the Earth. His knowledge of the size of Egypt after many generations of surveying trips for the Pharaonic bookkeepers gave a distance between the cities of 5000 stadia (about 500 geographical miles or 800 km). This distance was corroborated by inquiring about the time that it takes to travel from Syene to Alexandria by camel. 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. The common Attic stadion was about 185 m,[9] which would imply a circumference of 46,620 km, i.e. 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion"[10] of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 2%.
Although Eratosthenes' method was well founded, the accuracy of his calculation was limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is slightly north of 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. Given the margin of error for each of these aspects of his calculation, the accuracy of Eratosthenes' size of the Earth is surprising.
Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earth's size was accepted for hundreds of years afterwards. His method was used by Posidonius about 150 years later.
Sources: Eratosthenes
· Thomas Little Heath, A History of Greek Mathematics (2 vols.)
· (Oxford, 1921)
http://en.wikipedia.org/wiki/Eratosthenes
