Eratosthenes' Shadow (240 BCE)
📐 Measuring the Earth
Question
How could anyone know the size of the Earth before satellites, planes, or even maps?
Around 240 BCE the librarian Eratosthenes knew two facts: at noon on the summer solstice, the Sun was directly overhead in Syene (modern Aswan) - a vertical pole cast no shadow - while in Alexandria, due north, a pole cast a shadow. The shadow angle was about 7.2 degrees, which is 1/50th of a full circle. If the distance between the cities (about 5,000 stadia) is 1/50th of the Earth's circumference, then the whole circumference is 50 times that distance. One angle, one distance, and the size of the planet.
The math
C = d × (360° ÷ θ) = 5,000 stadia × (360° ÷ 7.2°) = 250,000 stadia. With a stade of 157.5-160 m that is 39,375-40,000 km - within about 2% of the modern 40,075 km (NASA).
Why it matters
No observation alone can tell you the size of the Earth - you need geometry. The same idea (measure an angle, know a distance) is behind triangulation, surveying, and every GPS fix your phone makes today.