The Approximate History of Area and Volume
Early calculations of area and volume are explained. It is shown that in ancient Egypt, use of regular shapes was needed to divide up land following annual flooding from the Nile. It is explained that the same principle of using regular shapes helped calculate volumes, for example to work out amounts of building materials needed for different structures.
The importance of the ancient Greeks in making major advances in geometric calculations is shown through a bank-heist style sketch featuring Archimedes. A basic version of the method of exhaustion is shown as a way of calculating the area of a circle by subscribing it with many-sided polygons. As a further step, it is shown that the volume of a sphere can be calculated by dividing the sphere into a series of slim cylinders, the volumes of which can then be added together. The equation for the volume of a sphere based on pi is introduced by the Chinese mathematician Zu Gengzhi.