Episode 6: Area of a Circle [#MathChops]

This problem of determining the area of a circle, or better defined as the area inside of a circle, was a huge dilemma in the field of mathematics. It was not until the mid 200's BC when Archimedes began to anticipate modern calculus and analysis though concepts of infinitesimals and exhaustion, which he used to solve this major challenge of finding the area of a circle.

Archimedes' method of finding the area is described as "squaring the circle", which is trying to find the square that has the same enclosed area as a circle of a given radius. Using this and also using a method where he approximated the area of a circle with other, known shapes such as squares and hexagons, Archimedes was able to determine the area inside of a circle. Take a look at the proof to see how Archimedes came up with the formula we know today: