Eratosthenes Calculates the Circumference of the Earth
Around 240 BCE, Eratosthenes of Cyrene, who had been appointed Chief Librarian of the great Library of Alexandria by Ptolemy III, performed one of the most elegant experiments in the history of science using nothing more than a stick, a well, and the geometry of shadows. Eratosthenes had read that at the town of Syene (modern Aswan) in upper Egypt, on the summer solstice at noon, the sun shone directly down a deep well, meaning it was directly overhead with no shadow. In Alexandria, some 800 kilometres to the north, the same moment produced a shadow of measurable angle. He had a vertical rod, or gnomon, erected in Alexandria and measured the shadow angle as approximately 7.2 degrees, or one-fiftieth of a full circle. The geometric reasoning that followed was beautifully simple: if the sun is far enough away that its rays are effectively parallel, and if Alexandria and Syene lie on the same meridian, then the angle between the two sun-directions must equal the angle subtended by the arc between the two cities at the centre of the Earth. Seven point two degrees is one-fiftieth of 360 degrees. Therefore the Earth's circumference is fifty times the distance between Alexandria and Syene. Eratosthenes estimated that distance, probably using bematists (professional pacers employed by Alexander and the Ptolemies to measure road distances), at about 5,000 stadia. His resulting figure for the Earth's circumference, somewhere between 39,375 and 46,620 kilometres depending on which stadion he used, compares to the modern value of 40,075 kilometres. The most plausible interpretations put his error below 2 percent — a stunning achievement. This was not Eratosthenes's only geodetic triumph. He also calculated the tilt of the Earth's axial obliquity with remarkable accuracy and made an estimate of the distance from the Earth to the Sun. He developed a sieve for identifying prime numbers (the Sieve of Eratosthenes) that remains the simplest pedagogical method today. He produced the most accurate map of the known world to date, extending from Britain to India, and coined the word geography. His contemporaries nicknamed him Beta, suggesting he was second-best in every field — a mathematician inferior to Archimedes, a poet inferior to Callimachus, a historian inferior to others. Modern assessment is kinder: Eratosthenes was the founding father of mathematical geography, and his measurement of the Earth stands as one of antiquity's most precise scientific achievements. He reportedly died around 194 BCE, having gone blind in old age and choosing to end his life by voluntary starvation. The Library he had served for decades would endure, in various forms, for several more centuries.
- Year: 240 BCE
- Category: Scientific
