The first precise determination of the size of the Earth is ascribed to which Egyptian scholar?

The first precise determination of the size of the Earth is ascribed to which Egyptian scholar?

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

Answer: (D)

Estimating Earth's size hinges on using simple geometry with the fact that the Sun’s rays are nearly parallel at large distances. In Alexandria, Eratosthenes compared shadows at the same time in two places: in Syene (Aswan) the Sun was directly overhead on the solstice, so there was little to no shadow, while in Alexandria there was a measurable shadow, indicating the Sun was at an angle. He measured that angle to be about 7.2 degrees, which is roughly 1/50 of a full circle. If the distance between the two cities is about 800 kilometers, that distance represents about 1/50 of Earth’s circumference. Multiply by 50 to get the full circumference, yielding around 40,000 kilometers—closely matching the true value. This elegant result rests on Earth’s sphericity and the parallel Sun rays assumption, and it marks a pioneering use of geometry to size the planet. Other figures contributed to mathematics and astronomy, but Eratosthenes is the one credited with this specific measurement in ancient times.

Estimating Earth's size hinges on using simple geometry with the fact that the Sun’s rays are nearly parallel at large distances. In Alexandria, Eratosthenes compared shadows at the same time in two places: in Syene (Aswan) the Sun was directly overhead on the solstice, so there was little to no shadow, while in Alexandria there was a measurable shadow, indicating the Sun was at an angle. He measured that angle to be about 7.2 degrees, which is roughly 1/50 of a full circle. If the distance between the two cities is about 800 kilometers, that distance represents about 1/50 of Earth’s circumference. Multiply by 50 to get the full circumference, yielding around 40,000 kilometers—closely matching the true value. This elegant result rests on Earth’s sphericity and the parallel Sun rays assumption, and it marks a pioneering use of geometry to size the planet. Other figures contributed to mathematics and astronomy, but Eratosthenes is the one credited with this specific measurement in ancient times.