The Impact Of Mathematics On The Physical Sciences

The Impact of Mathematics on the Physical Sciences

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 ArchimedesÐ'ÐŽÐ'Ї time, he was most memorable for his mechanical innovations such as the Ð'ÐŽÐ'oClaw of ArchimedesÐ'ÐŽÐ'± or Ð'ÐŽÐ'oship shakerÐ'ÐŽÐ'±. Plutarch described these machine as Ð'ÐŽÐ'ohuge poles thrust out from the [city] wallsÐ'ÐŽÐ'±, 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, Ð'ÑžÐ"' 10). According to a translated twelfth century book, Archimedes is reported to have constructed a reflective device to focus the sunÐ'ÐŽÐ'Їs rays on the prow of the Roman ships, which purportedly set them on fire (Tzetzes, c.12th century). Plutarch also relates an incident about ArchimedesÐ'ÐŽÐ'Ї 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, Ð'ÐŽÐ'owith 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 seaÐ'ÐŽÐ'± (O'Connor & Robertson, 1999, Ð'ÑžÐ"'14). 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 Ð'ÐŽÐ'osordid and ignobleÐ'ÐŽÐ'± when applied Ð'ÐŽÐ'ofor use or profitÐ'ÐŽÐ'± (O'Connor & Robertson, 1999, Ð'ÑžÐ"'16). Yet Archimedes is quoted in a translation of The Method to attest to the value he gained from his inventions, Ð'ÐŽÐ'oÐ'ÐŽÐ'¦certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards Ð'ÐŽÐ'¦. 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 knowledgeÐ'ÐŽÐ'± (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 Ð'ÐŽÐ'ogave birth to the calculus of the infiniteÐ'ÐŽÐ'± (O'Connor & Robertson, 1999, Ð'ÑžÐ"'22). In a work that was later lost he is reported to have given the value of Ð'ҐÐ"o at 3.141596, which remained the most accurate estimate for another 1600 years (O'Connor & Robertson, 2000). In the Sandrekoner, he described his place-value system with a base of 100 million to express large numbers, such as the grains of sand needed to fill the Universe. He also described his method of measuring the sunÐ'ÐŽÐ'Їs diameter and the heliocentric solar system of Aristarchus. He developed theorems regarding the center of gravity of plane figures and solids. He is most famous for his principle of hydrostatics, which states that a volume of a solid immersed in fluid is equal to the volume of the fluid displaced. His greatest discovery is considered the relation between the surface area and volume of a sphere and its circumscribing cylinder (Archimedes, 2007). Archimedes, too, ranked this his highest achievement and requested that its representation be inscribed on his tomb.

ArchimedesÐ'ÐŽÐ'Ї treatises include 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 Sandreckoner. In 1899 a 10th century manuscript known as a palimpsest, which contained a Greek copy of four of ArchimedesÐ'ÐŽÐ'Ї works including The Method, was identified to be part of the Library of the Holy Sepulchre in Istanbul. In this work, Archimedes explained how he discovered his geometrical results. There are still many works of Archimedes, which are currently lost from antiquity. Some of his treatises were translated into Arabic in the eighth and ninth centuries, but the greatest influence of Archimedes on later mathematicians was not seen until the 16th and 17th centuries when some of his works were translated from Greek into Latin to be captured by the fertile minds of Kepler and Galileo.

Isaac Newton

Isaac Newton is considered to be an important mathematician and physicist, and is regarded as a founding examplar of modern physical science. He was born in England on December 25, 1642. He began attending Trinity College Cambridge in 1661 and graduated in 1665. Newton was elected a Fellow of Trinity College in 1667, and in 1669 became a Lucasian Professor of Mathematics. He became Master of the Mint in 1699. He was elected a Fellow in 1671 and President