On the day of the summer solstice, at noon, Eratosthenes was aware of a deep well on the Nile close to Aswan where the sun shone all the way to the bottom. Because the sun was not overhead in Alexandria, the length of that shadow was not zero.
We believe that the light rays from the sun that reach us are all traveling in the same direction; they are parallel, as the sun is thought to be extremely far away. No shadow would be formed by a vertical stick at point A, a "moderate" shadow by a stick at point B, and a very long shadow by a stick at point C. A radius of the earth leading to point A is shown on the diagram, and another leading to point B. A little geometry reveals that the angle between those two radii and the difference between the shadow angles are the same. In our example, the shadows indicate that during our journey from Florida to Pennsylvania, we had rotated the earth by about 10 degrees.
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