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If the sun is directly overhead at Syene on the solstice, then the simultaneous angle of the sun’s shadow back at Alexandria, a, must by definition be the same as the angle 3 between two lines drawn from the earth’s center to Syene and Alexandria.

It assumes that the well in Syene was sunk perpendicularly to the surface of the earth.

Eratosthenes knew that the distance between Alexandria and Syene was approximately 800 kilometers, because he hired a man to pace it out.

This: A flat map of ancient Egypt; when the sun is directly overhead, vertical obelisks cast no shadows in Alexandria or Syene.

For the observed difference in the shadow lengths, the distance between Alexandria and Syene had to be about seven degrees along the surface of the Earth; that is, if you imagine the sticks extending down to the center of the Earth, they would there intersect at an angle of seven degrees.