Eyes, Feet, Sticks, and Brains

In the ancient Mediterranean city of Alexandria, at times the world's greatest and smartest city and keeper of the largest collection of knowledge in the Alexandrian Library, lived one of the librarians of the great collection, Eratosthenes.

This guy liked to read, and one day he came across a passage that struck him. It read that in the city of Syene, south of Alexandria, on the summer solstice, the longest day of the year, at high-noon posts cast no shadows and a deep well is fully illuminated, phenomena that doesn't otherwise happen.

This piqued Eratosthenes. He planned to check the shadows in Alexandria at the same time on the next summer solstice. He even paid a man to walk the distance from Alexandria to Syene to get as accurate of a reading of the distance between those two places.

After the next solstice Eratosthenes had the data he wanted. The distance between the cities has been translated to about 800 km, and the angle between the posts perpendicular to the ground was calculated to be 7 degrees; that is, is each post was extended down to the Earth's center, the angle created by those lines would be seven degrees.

Knowing that a circle is 360 degrees, and 7 being about a fiftieth of that number, Eratosthenes multiplied the 800 km by 50, generated the number 40,000 km.

The actual circumference of the Earth is 40,007.863 km.

Pretty good use of eyes and feet and sticks and brains.