What is the radius of the earth

Who Was Eratosthenes?

Eratosthenes was born around 276 BC. Born in Cyrene (today Shahhad, Libya). He died around 195 BC. In Alexandria (Alexandria is marked with 'A' on the right of the two maps.).
Eratosthenes was a pupil of Callimachus, a friend of Archimedes and himself one of the greatest scientists of his time. Among other things, he dealt with geography, astronomy and mathematics. He designed a map of the world with the help of a coordinate network of parallel circles and meridians, set up a star catalog with 675 stars and invented a method for finding prime numbers: the 'Sieve of Eratosthenes'. In addition, Eratosthenes is regarded as the founder of chrononology and scientific geography. And he headed the famous library of Alexandria1) Meyer's great pocket dictionary, Large lexicon of astronomy by Joachim Herrmann (Mosaik-Verlag)

None of the sources available to me show whether Eratosthenes calculated the angle gamma after measuring the length of the shadow of the column or whether he measured the angle alpha. In any case, he knew that the central angle beta had to be the same size as gamma (gamma and beta are alternating angles at intersected parallels, the sun rays) or alpha (alpha and beta are step angles at intersected parallels, the sun rays).
Eratosthenes determined alpha (or gamma) to be about 1/50 of a full angle. Beta therefore also had to make up 1/50 of 360 °. So the length of the 'route' AS from Alexandria to Syene had to fit approx. 50 times into the desired circumference of the earth. Eratosthenes only needed this distance from Alexandria to Syene to roughly determine the circumference of the earth.
One reads that Eratosthenes should have asked a friend to determine this distance. The measurement showed that Syene was 5,000 stadiums (1 stadium was 157.5 m) from Alexandria. According to Eratosthenes, the circumference of the earth had to be 50 * 5,000 stadia = 250,000 stadia or 50 * (5000 * 157.5 m) = 39,375,000 m = 39,375 km long.
(Source: http://www.wernerpieper.de/schmath/erl_erat.htm)