History

Archimedes of Syracuse is considered by many to be one of the greatest mathematicians of all time. Besides mathematician, Archimedes was also known as an astronomer, engineer, physicist and inventor.

Archimedes books entitled, "On the Sphere and Cylinder." and "The Method of Mechanical Theorems" both investigate the surface area of a sphere and the volume of a sphere, respectively. Both of these proofs are seen as predictive of the ideas in integral calculus. To derive the formula for the surface area of a sphere Archimedes employs what is known as "The method of exhaustion." The method that Archimedes employs to find the formula for the volume of a sphere is know popularly as "The Method." Both of these proofs are investigated in the Mathematics section.

Eudoxus of Cnidus was an important mind in mathematics about two centuries before Archimedes. He was a scholar, mathematician and astronomer. In mathematics one of his most notable contributions is his popularization of the method of exhaustion that he and other mathematicians used to find areas and volumes of objects. It is believed that he is the main source of the proof of the volume of a cone that Euclid included in his collection of theorems known as Euclid's Elements.

Bonaventura Cavalieri was an Italian Mathematician who had quite an impact on the preliminary ideas for integral calculus. One of these ideas that this website explores more deeply is called the Cavalieri Principle. Archimedes did not have the luxury of the Cavalieri Principle, he still used something equivalent to it in his derivation for the volume of a sphere.


Archimedes Image retrieved from http://commons.wikimedia.org/wiki/File:PSM_V78_D337_Archimedes.png and is considered to be a public domain file via Wikimedia Commons.