So how did Eratosthenes figure out how big around the Earth is? Here’s how:
First, he assumed the Earth is round like a ball.
Second, he knew several things about a little town called Syene. It is 5,000 stadia (575 miles or 925 kilometers) directly south of Alexandria. There was a well in the center of town, dug deep and plumb—straight toward the Earth’s center. At noon on June 21st, the Summer solstice, you could see the Sun reflected on the water way down in that well, which means the Sun is directly overhead.
That’s because Syene is located on the Tropic of Cancer. If you happen to be standing on the Tropic of Cancer and it’s noon where you are on June 21 you can draw a straight line from the center of the Earth, through the Tropic of Cancer, to the Sun.
A stadion is an ancient Greek unit of measurement—it’s 600 feet (an eighth of a mile). Stadion is singular (nominative, singular, second declension); stadia is plural (nominative, plural, second declension). 5,000 stadia = 575 miles or 925 kilometers. I hope I declenched in all the right spots. Many thanks to my Greek-scholar pals Jackie J., Michele J. & Joann W!