Intro

Many great mathematicians of the past had an impact on physical sciences. This paper will discuss the historical background, respective times, and contemporary and modern societal contributions of three of those mathematicians: Archimedes of Syracuse, Isaac Newton, and Leonhard Euler. Archimedes of Syracuse

Archimedes was born in a Greek city-state of Syracuse, Sicily in 287 BC. He was killed during a Roman incursion in 212 BC during the Second Punic War. Archimedes was purportedly largely responsible for the defense of Syracuse as they held the Romans off for two years with the use of his war machines. Most of the information we currently have about Archimedes is anecdotal. Important figures such as Plutarch immortalized Archimedes in their own works and their many references to his discoveries, mathematical theories, and brilliant mechanical innovations. In Archimedes¡¯ time, he was most memorable for his mechanical innovations such as the ¡°Claw of Archimedes¡± or ¡°ship shaker¡±. Plutarch described these machine as ¡°huge poles thrust out from the [city] walls¡±, which either dropped heavy weights down upon the attacking Roman ships sinking them or lifted these ships so that they would plunge poop deck-first into the sea. At times, they lifted ships high into the air and waved them about until all the mariners had fallen into the sea (O'Connor & Robertson, 1999, ¢Ò 10). According to a translated twelfth century book, Archimedes is reported to have constructed a reflective device to focus the sun¡¯s rays on the prow of the Roman ships, which purportedly set them on fire (Tzetzes, c.12th century). Plutarch also relates an incident about Archimedes¡¯ demonstration of his compound pulley. King Hieron of Syracuse requested that Archimedes demonstrate the practical application of his scientific discoveries so that common people could appreciate the usefulness of his science. Archimedes used his compound pulley system to draw a ship, which was fully weighted with cargo and passengers, from the dock. He did this, Plutarch states, ¡°with no great endeavour, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly as if she had been in the sea¡± (O'Connor & Robertson, 1999, ¢Ò14). Another invention, the Archimedes screw, was a form of hand driven water pump, in which an internal screw within a cylinder could divert water up and away from a flooded area. An archetype of this was thought to be used to irrigate the hanging gardens of Babylon millennia earlier (Rorres,1995). He also improved the power and accuracy of the catapult. He developed an odometer which measured traveled distance in mile increments using a gear mechanism that would drop a ball every mile into a bucket. Although Archimedes received great recognition for these ingenious and awe-inspiring innovations, he considered it ¡°sordid and ignoble¡± when applied ¡°for use or profit¡± (O'Connor & Robertson, 1999, ¢Ò16). Yet Archimedes is quoted in a translation of The Method to attest to the value he gained from his inventions, ¡°¡¦certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards ¡¦. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge¡± (O'Connor & Robertson, 2006). Archimedes is held by most historians to be one of the greatest mathematicians in all history. His method of integration perfected the calculation of areas, volumes, and surface areas and ¡°gave birth to the calculus of the infinite¡± (O'Connor & Robertson, 1999, ¢Ò22). In a work that was later lost he is reported to have given the value of ¥ð at 3.141596, which remained the most accurate estimate for another 1600 years (O'Connor & Robertson, 2000). In the...