The legendary Ancient Greek astronomer and the mathematician Erastofen by practical consideration defined a tilt angle of the Sun to Earth in two cities lying, according to him, on one meridian. Knowing distance between them, it mathematically calculated the radius of our planet. Calculations were quite exact.
Erastofena method
Erastofen lived in the city of Alexandria located in the north of Egypt near the mouth of the Nile River on the coast of the Mediterranean Sea. He knew that in a certain day every year in the city of Siena in the south of Egypt at the bottom of wells there was no solar shadow. That is the Sun at that moment is directly over the head.
However in Alexandria which was located to the north of Siena even in day of a summer solstice the Sun never happens directly over the head. Erastofen understood what can be defined as far as the Sun is displaced from situation "directly over the head", having measured the corner formed by a shadow from a vertical object. He measured shadow length from a high tower in Alexandria and, using geometry, calculated a corner between a shadow and a vertical tower. It was equal about 7.2 degrees.
Further Erastofen used more difficult geometrical constructions. Assumed that a corner from a shadow just the same, as between Alexandria and Siena if to consider from the center of Earth. For convenience considered that 7.2 degrees are made by 1/50 part of a cycle. To find Earth circle length, it was necessary to increase distance between Siena and Alexandria by 50. According to Erastofen, the distance between the cities made 5 thousand stadiyev. But the general unit of length those far times did not exist, and today it is unknown to what stages Erastofen used. If he applied the Egyptian, making 157.5 m, the radius of Earth equaled 6287 km. The error in that case was 1.6%. And if used more widespread Greek stages, equal 185 m, the error would make 16.3%. Anyway accuracy of calculations quite good for those times.
Biography and scientific activity of Erastofen
It is considered that Erastofen was born in 276 B.C. in the city of Cyrene which was in the territory of modern Libya. Studied within several years in Athens. Carried out a considerable part of the adulthood in Alexandria. Died in 194 B.C. at the age of 82 years. According to some versions, starved himself to death after went blind. Long time Erastofen headed the Alexandria library, the best-known library of the ancient world. Besides that he calculated the size of our planet, made some more important inventions and opening. Invented a simple method to define prime numbers, called now "Erastofen's sieve". Drew "world map" in which showed all parts of the world known at that time to ancient Greeks. The card was considered as one of the best for the time. Developed the system of longitude and width and the calendar including leap-years. Invented the armillyarny sphere, the mechanical device used by early astronomers to show and predict apparent motion of stars in the sky. Also made the star catalog including 675 stars.