If you had to prove that the earth is round right now, how would you do it? I will give you an example below, and a mystery that maybe you can solve. You’ll see that living in Greece helps if you want to discover the earth is round!

How did people first realize the Earth is round? The first measurement of the circumference of the earth is often attributed to Eratosthenes, a Greek mathematician and philosopher. He used the fact that the length of the shadow of a vertical stick at noon time is different at different latitudes.
He assumed the sun’s rays were parallel and interpreted his findings as being due to a curvature to the earth’s surface. He however could not have known that the suns rays are parallel and his findings could just as easily have been interpreted to be due to a finite (not infinite) distance to the sun.

How did Eratosthenes know which interpretation to pick? Though I had known the answer for some time, on a recent visit to the Greek isles, I was confronted with the answer in a vivid way: from most of the island you can see a nearby island on the horizon! In a country like that, how can you not be drawn to develop the art of seafaring? The fact is, every sailor in Greece knew that the earth is round, and so did their girlfriends and wives! As they watched a sailor set off from home, the keel of his ship would dip below the horizon while the large sails where visible for many more miles. The sailor on the other hand would see the tall mountains of his home island long after the shoreline from which he departed had disappeared from sight. This is due to the curvature of the earth’s surface.

Here is a photo of the see taken from the island of Crete.

From an altitude of about 30 meters, the island Santorini off the coast of Crete, Greece, is barely visible.

This picture is taken at an altitude of about 30 meters above sea level. If you look very closely you can see the nearby island of Santorini on the horizon. After some meddling with the contrast, we can see the island quite clearly.  If we walk down the hill to the shoreline however, the island has disappeared from view!

From the shoreline, no island is visible!

This observation lends itself to a land based measurement of the radius of the earth. If you are standing on the beach and you know the height and distance of a distant object that has just barely disappeared from view, the radius of Earth is given (approximately) by

Where R is the radius of the earth, d is the distance to the far away island, and h is its height (derivation here). For the purpose of this calculation I just looked up the distance and height of the distant island, though this information would probably have been available to the ancient Greeks as well.

Using d = 114 km and h = 584 m we get

R = 11126 km

This radius is about a factor of 2 too large! The right answer would have been 6,378.14 km. The challenge is to all you scientists and would be scientists to tell me what I missed. I can tell you this: I did not miscalculate.