(They also) make sense on a flat Earth. But how could it be, Eratosthenes asked, that at the same instant there was no shadow at Syene and a very substantial shadow at Alexandria. The only answer was that the surface of the Earth is curved. Not only that, but the greater the curvature, the bigger the difference in the lengths of the shadows. The sun is so far away that its rays are parallel when they reach the Earth, sticks at different angles to the sun's rays will cast shadows at different lengths. For the observed difference in the shadow lengths, the distance between Alexandria and Syene had to be about 7 degrees along the surface of the Earth. By that, I mean, if you would imagine these sticks extending all the way down to the center of the Earth, they would there intersect at an angle about seven degrees. Well, seven degrees is something like a 50th of the full circumference of the Earth, 360 degrees. Eratosthenes knew the distance between Alexandria and Syene. He knew it was 800 kilometers. Why? Because he hired a man to pace out the entire distance so that he could perform the calculation I'm talking about. Now 800 kilometers times 50 is 40,000 kilometers. So that must be the circumference of the Earth. That's how far it is to go once around the Earth. That's the right answer. Eratosthenes' only tools were sticks, eyes, feet and brains, plus a zest for experiment. With those tools he correctly deduced the circumference of the Earth to high precision with an error of only a few percent. That's pretty good figuring for 2200 years ago.

Then, as now, the Mediterranean was teeming with ships, merchantmen, fishing vessels, naval flotillas, but there were also courageous voyagers into the unknown. 400 years before Eratosthenes, Africa was circumnavigated, by a Phoenician fleet in the employ of the Egyptian Pharaoh Necho. They set sail probably in boats as frail and open as these out from the Red Sea down east coast of Africa, up into the Atlantic and then back through the Mediterranean. That epic journey took three years about as long as it takes Voyager to journey from Earth to Saturn. After Eratosthenes some may have attempted to circumnavigate the Earth. But until the time of Magellan no one succeeded. What tales of adventure and daring must earlier have been told as sailors and navigators, practical men in the world, gambled their lives on the mathematics of a scientist from ancient Alexandria.

Today Alexandria shows few traces of its ancient glory of the days when Eratosthenes walked its broad avenues. Over the centuries waves of conquerors converted its palaces and temples into castles and churches, then into minarets and mosques. The city was chosen to be the capital of his empire by Alexander the Great on a……