Archimedes

The king had given a goldsmith a set amount of gold and it was all to be used to make a solid gold crown. When Archimedes filled his bathtub brim full, he realized the mass of water that overflowed was proportional to the mass of his body that was placed into the tub. This realization is known as the Archimedes" Principle. He was so excited when he made this discovery that he ran down the streets of Syracuse naked, shouting "Eureka! Eureka!" (I have found it!) . The next day he placed the crown in a full tub of water. There turned out to be more water displaced than there should have been, which means the crown contained another substance, possibly silver (10.2. Archimedes shu). .
             King Hieron also asked him to move a boat on his own that would have taken many men to do. Archimedes moved the ship easily all by himself using combinations of pulleys. Although he had many good mechanical inventions, he enjoyed mathematical theory more. He was often so into his geometry that his servants would force him to get into a bathtub and, even while his servants anointed him with oils and perfumes, he would try to draw geometric diagrams on his body in the oil on his skin. He often would be so intent in working out problems that he would forget to eat. He worked a lot with integration to find areas, volumes and surface areas of many objects. Chasles claimed that Archimedes" work with integration brought on the start of Calculus and was then brought to perfection by Cavalieri, Fermat, Leibniz, and Newton (Archimedes of Syracuse. groups). He determined the exact value of to be between the values of 3 and 3 . He figured this much out by circumscribing and inscribing a circle with.
             regular polygons having 96 sides (Archimedes of Syracuse. math). He also showed he could approximate square roots accurately. .
             Some of the books he has written are as follows: On plane equilibriums, Quadrature of the parabola, On the sphere and cylinder, On spirals, On conoids and spheroids, On floating bodies, Measurement of a circle, and The Sand Reckoner.