Which ancient thinker calculated the Earth's circumference?

• A. Euclid
• B. Archimedes
• C. Eratosthenes
• D. Ptolemy

Answer: (C)

This question tests how geometry and astronomical observation can determine the size of the Earth. Eratosthenes compared the angle of the sun at two places at the same time. In one city, the sun was directly overhead at noon, casting no shadow, while in another city at the same moment the sun stood at an angle and cast a measurable shadow. The angle between those sun directions was about 7.2 degrees, roughly 1/50 of a full circle. He also knew the distance between the two cities, about 5,000 stadia.

Since the sun’s rays are effectively parallel, that angle corresponds to the central angle subtending the arc between the two locations on Earth. The circumference is proportional to this arc: circumference equals distance times 360 divided by the angle. With a 7.2-degree angle, 360 divided by 7.2 is about 50, so the circumference comes out to roughly 50 × 5,000 = 250,000 stadia. Depending on the exact length of a stadium, this estimate aligns surprisingly well with the real Earth circumference.

So, Eratosthenes is the thinker who performed this calculation, using a simple geometric argument linked to observations of the Sun.