Archimedes

             Being born the son of Phidias, a well-known astronomer, he learned under the teachings of Euclid, the Greek mathematician in his school at Alexandria.
             Archimedes spent most of his entire life in his birthplace Syracuse. He was a master at mathematics and spent most of his time contemplating new problems to solve, becoming at times so involved in his work that he forgot to eat. He used any available surface, from the dust on the ground to ashes from an extinguished fire, to draw his geometric figures. Never giving up an opportunity to ponder his work, after bathing and anointing himself with olive oil, he would trace figures in the oil on his own skin.
             One famous story was when Hiero ordered a gold crown from the goldsmith and gave the goldsmith the exact amount of gold to make it. When the king received the crown he suspected that the goldsmith may have substituted some silver and kept a portion of the gold. Unable to prove the goldsmith wrong he submitted his quandary to Archimedes. A while later while still stumped over what he should do Archimedes slipped into his bathtub to bathe. Upon entering the tub he noticed that the water level in the tub was directly proportional to the mass of his body that was submerged in the tub. This principle became known as Archimedes principle and gave him the means to solve the king's problem with the gold crown. Upon his discovery his excitement was so high that he ran out into the streets shouting "Eureka Eureka!- Archimedes in his time also proved his lever theory, invented the water screw, built the first compound pulley, calculated the value of PI between 3 ½ and 3 10/71, and built a miniature planetarium. .
             Throughout his life Archimedes had invented many things, however it has been documented that Archimedes felt that his calling was directed towards the purely theoretical fields in Mathematics and Geometry. Well know for his approximation of the value of PI and for devising new ways for approximating square roots, his greatest achievements were his theories in Integral Calculus.