What Are Some Interesting Facts About Shadows?

The first person to calculate the size of the planet Earth with a high degree of accuracy used simple geometric equations and measurements of shadows. Eratosthenes, the head librarian of the Great Library of Alexandria, performed this feat over 2,000 years ago, around 250 BCE.

Although many cultures held the belief that the world was flat well into the Middle Ages, the hypothesis of a spherical globe has existed for over 2,000 years. Using basic principles of Euclidean geometry, Eratosthenes of Alexandria calculated the circumference of the planet Earth in the year 250 BCE.

Eratosthenes noticed that the length of shadows cast by similar objects at the same moment in time varied depending on the location of those objects on the surface of the Earth. From this, he reasoned that the surface of the world must be curved; if the world was a flat plane, two similar objects would cast similar shadows regardless of their location.

Eratosthenes first created accurate measurements of the length of shadows of two similar objects in two different cities at the same time. Then, he hired a man to measure the distance between these two cities by walking from one to the other and then counting his steps. By comparing the shadows’ lengths, Eratosthenes reasoned that the distance between these two cities (about 800 km) was seven degrees out of the 360 degrees that represented the circumference of the Earth. Since seven degrees is roughly the equivalent of 1/50 of 360 degrees (the number of degrees inside a full circle), Eratosthenes calculated that the distance between the two cities was about 1/50 of the circumference of the Earth. This led him to conclude that the Earth’s circumference was 40,000 km, which is about 99.8 percent accurate. The actual circumference of the planet, measured many centuries later, is 40,075 km.