The Greek mathematician who estimated Earth’s circumference using solstice sunlight at Syene and Alexandria was Eratosthenes.
Eratosthenes, who lived in the third and second centuries BCE, was a scholar associated with the Library of Alexandria. He learned that at noon on the summer solstice, sunlight reached the bottom of a deep well at Syene, identified with modern Aswan, while vertical objects at Alexandria still cast shadows. That difference showed that the Sun’s rays were striking the two cities at different angles because Earth is curved.
His reported shadow angle was about 7.2 degrees, or one-fiftieth of a circle. Eratosthenes paired that fraction with an estimated distance of roughly 5,000 stadia between the cities, multiplying by 50 to obtain approximately 250,000 stadia for Earth’s circumference. The exact modern conversion of a stadion is uncertain, but the result was remarkably close to the real size of Earth.
The method was elegant but not perfect. Syene was not exactly on the Tropic of Cancer, and it was not precisely due south of Alexandria. Those errors happened to offset one another to some extent. The experiment is therefore remembered both as an early triumph of mathematical geography and as a model of how geometry can measure a planet.