#58 -240 · Eratosthenes, Library of Alexandria · Science / measurementproxy-test
Eratosthenes measured the size of the entire planet without ever leaving Alexandria
the problem
A quantity seemed to require travel, instruments, or observation nobody in the ancient world had access to
background
By the 3rd century BCE, educated Greeks accepted the Earth was a sphere, but nobody had a way to say how big it was — the obvious method, circumnavigating or otherwise physically traversing the whole planet, was wildly beyond the technology and organization of the era. Eratosthenes, running the Library of Alexandria, had access to travelers' reports and geographic records but no instrument capable of surveying a curve that large directly.
He had one useful fact on hand: at noon on the summer solstice in Syene (modern Aswan), sunlight reportedly reached straight to the bottom of a deep vertical well, meaning the sun sat directly overhead there at that exact moment. Nobody before him had thought to pair that isolated travelers' curiosity with a second, ordinary measurement taken somewhere else at the same moment.
the move
On the same solstice noon, Eratosthenes measured the angle of the shadow cast by a vertical stick (a gnomon) in Alexandria and found it about 7.2 degrees off vertical — Syene's well proved the sun was at zero degrees there. Since Alexandria and Syene lay roughly on the same meridian, that 7.2-degree gap was exactly the curvature of the Earth between the two cities, one-fiftieth of a full circle; multiplying that fraction by the distance between them, paced out by professional bematists at about 5,000 stadia, gave the Earth's total circumference.
the payoff
Eratosthenes' result of roughly 250,000 stadia converts, depending on which ancient stadion length is used, to somewhere between about 39,000 and 46,000 km against a true equatorial circumference of 40,075 km — a result within a few percent of correct, obtained with a stick, a well, and a distance paced out on foot.
what came after
The method is taught today as one of the founding demonstrations of geodesy and is still reproduced in classrooms as a hands-on shadow experiment; it stands as the standard historical example of deriving an apparently unmeasurable global quantity from two cheap, purely local, simultaneous observations.
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references
- [1]EratosthenesWikipedia, 2026en.wikipedia.org
- [2]How Eratosthenes Measured The Earth's Circumference With A Stick In 240 BCEIFLScience, 2023iflscience.com