On our last program we discussed a simple experiment run by an Alexandrian named Eratosthenes in the third century B.C.    By noting that, at the same time of day, sticks in the ground cast different-length shadows depending on whether they were in a northern or a southern town, Eratosthenes deduced that the surface of the earth must be curved -- and thus that the earth itself must be shaped like a ball.

This is an impressive enough achievement, but Eratosthenes didn't stop there. Realizing the earth was round, he then applied a little geometry. He imagined his two sticks -- one in the northern town of Syrene, one in the southern town of Alexandria -- as lines extending downward until they meet at the center of the earth.

Drawing more lines coming straight down to represent sunlight, Eratosthenes moved one stick along the outside of the circle until the shadow it would be casting matched the shadow his stick actually made. Now he knew how much of the circle extended between Syrene and Alexandria -- about seven degrees.

There's no fancy way to get around the next step: Eratosthenes needed to know the actual distance from Alexandria to Syrene. So he paid some camel caravan drivers to go from one town to the other and tell him how far it was. A few achy-footed camels later the answer came back: 500 miles. So, if 500 miles equals 7 degrees of the circle, the whole circle must be 25,000 miles.

Eratosthenes' answer, deduced with nothing but two sticks, some tired camels and a brain, is within a few percent of being correct.