prize7-2, Exercise 1: How Eratosthenes' method works

Model answer (check the details):

Idea: at noon on the summer solstice the sun was said to be directly overhead at Syene, so a vertical stick cast no shadow there. At the same moment in Alexandria a stick cast a shadow, measured as about one-fiftieth of a circle (about 7 degrees).

Steps:
1. The difference in the sun's angle equals the angle at the Earth's centre between the two places.
2. If 7 degrees corresponds to the distance between the cities, the whole circle (360 degrees) is about 50 times that distance.
3. Multiply the distance by 50 to get the circumference.

Assumptions:
- The Earth is a sphere.
- The sun is so far away that its rays arrive parallel.
- Syene and Alexandria lie on the same north-south line (roughly true but not exactly).
- The distance between the cities is known (it came from travel estimates).
- The length of the stadion used is known, which is uncertain today.

Takeaway: the method is sound, the inputs were rough, and the claim of great accuracy depends on which stadion is assumed.