Around 250 B.C., a Greek philosopher named Eratosthenes used an obelisk to calculate the circumference of the Earth. He knew that at noon on the Summer Solstice, obelisks in the city of Swenet (modern day Aswan) would cast no shadow because the sun would be directly overhead (or zero degrees up). He also knew that at that very same time in Alexandria, obelisks did cast shadows. Measuring that shadow against the tip of the obelisk, he came to the conclusion that the difference in degrees between Alexandria and Swenet: seven degrees, 14 minutes—one-fiftieth the circumference of a circle. He applied the physical distance between the two cities and concluded that the circumference of the Earth was (in modern units) 40,000 kilometers. This isn’t the correct number, though his methods were perfect: at the time it was impossible to know the precise distance between Alexandria and Swenet.

If we apply Eratosthenes’s formula today, we get a number astonishingly close to the actual circumference of the Earth. In fact, even his inexact figure was more precise than the one used by Christopher Columbus 1700 years later. Had he used Eratosthenes’s estimation, Columbus would have known immediately that he hadn’t reached India.

More examples are coming …