Mathematics -- to the Moon & Back Once upon a time, Alexander, a young man from Athens fell in love with a local girl, Adrianna, whose beauty was far greater than any other young woman he had ever seen. Alexander was so smitten with Adrianna that he promised her the moon. Being an astute girl, Adrianna told Alexander that she wasn't at all sure that he could deliver the moon, but he could begin to convince her that he was intelligent and clever by measuring the distance from the earth to the moon. Alexander had long heard the stories about his Greek ancestors who were experts in mathematics and astronomy, so he sought out some wise elders to learn more.

Alexander spent some time with two elders, one of whom told him he knew how to measure the size of the earth (which, Alexander mused, was bound to impress,...

Alexander grew more confident that he could win Adrianna's affections. Eratosthenes had lived for years in Alexandria, Egypt, and was prone to taking long walks -- and sometimes, camel rides. He often stopped by a deep well at midday, in the town of Syene, to refresh himself and his camel. On June 21 (in the third century B.C.), Eratosthenes noticed that the sunlight was reflected from the water at the bottom of the well. He had never seen this before, and giving it some thought, realized that on this day of the year, the sun was exactly vertically overhead. Interestingly, because Eratosthenes was an observant fellow, he knew that the sun never achieved a position of being exactly vertical over Alexandria. The next year -- precisely on June…