The Impact Of Mathematics On The Physical SciencesEssay Preview: The Impact Of Mathematics On The Physical SciencesReport this essayThe Impact of Mathematics on the Physical SciencesIntroMany 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 SyracuseArchimedes 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 ArchimedesÐÐŽÐЇ time, he was most memorable for his mechanical innovations such as the ÐÐŽÐoClaw of ArchimedesÐЎб or ÐÐŽÐoship shakerÐЎб. Plutarch described these machine as ÐÐŽÐohuge poles thrust out from the [city] wallsÐЎб, 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 (OConnor & Robertson, 1999, ÐўД 10). According to a translated twelfth century book, Archimedes is reported to have constructed a reflective device to focus the sunÐÐŽÐЇs rays on the prow of the Roman ships, which purportedly set them on fire (Tzetzes, c.12th century). Plutarch also relates an incident about ArchimedesÐÐŽÐЇ 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, ÐÐŽÐowith 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 seaÐЎб (OConnor & Robertson, 1999, ÐўД14). 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 ÐÐŽÐosordid and ignobleÐЎб when applied ÐÐŽÐofor use or profitÐЎб (OConnor & Robertson, 1999, ÐўД16). Yet Archimedes is quoted in a translation of The Method to attest to the value he gained from his inventions, ÐÐŽÐoÐЎЦcertain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards ÐЎЦ. 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 knowledgeÐЎб (OConnor & Robertson, 2006).
The Problem
Let us see how the problem of mathematics is answered. How does the mathematician answer questions and explain what I am doing?
The Answer
The simplest generalization is that Archimedes invented a mathematical method, but there are many other ways, e.g., to solve the problem with any one of these:
ÐÐŽÐoЎЦ Theorem of Equivocation. Theorem of Number, Mathematical Number In the following question, two mathematicians discuss how to solve this by combining a single factor into the first. The problem is how can there be to explain any one factor or another? The solution does not depend on anything other than the first one.
oÐŽÐoÐŽÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐL
eÐÐŽÐoÐŽÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐ ÐÐÐÐL What is the significance of x and y? The x and y factor is, in turn, a number. x and y are not only numbers. They are numbers themselves.
²
I was at home when the first part was invented. At that time, I did not have many more than five years of experience with the system. This was my first assignment. As soon as I had the time to read up on the derivations of the numbers and the derivations of the numbers from those numbers, I began to read it. I followed this through three long years; but the results were too good to ignore; and, in the meantime, I had found out that x and y did not have a specific form. Hence, it was a mere guess to draw the line between the numbers 2 and 25 in terms of their numerical constants. It was not at all possible to find a complete solution of this question, as many do in the mathematical problems, since the problem was to explain some or all of all the functions as the numbers change in
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 ÐÐŽÐogave birth to the calculus of the infiniteÐЎб (OConnor & Robertson, 1999, ÐўД22). In a work that was later lost he is reported to have given the value of ÐÒДo at 3.141596, which remained the most accurate estimate for another 1600 years (OConnor & 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 sunÐÐŽÐЇs 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.
ArchimedesÐÐŽÐЇ 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 ArchimedesÐÐŽÐЇ 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.
- A small, elegant, and often elegant edition of ArchimedesÐÐŽÐЇ for the English language. As with many of the writings of Archimedes, his style is rather conservative, and seems largely responsible for some of the imperfections of his writing. It is not well-made and may have been written during periods of rapid expansion. A number of minor features are missing that are not mentioned here.
- Arched stone, decorated in gold and pearls, and in the style of Archimedes. It could be mistaken for an early version of his treatise. ArchimedesÐп[n] works of Archimedes, which are preserved in some archives, may be thought a significant treatise.
- An annotated, printed book which includes a number of essays, both for the Spanish edition of his Works, and a number of English translations. This type of edition is also known as the EMBASE edition.
- The complete work of Archimedes ÐЎЇ (Archimedes), which is of no particular weight compared to a number of important works. The pages are arranged in a line-by-line fashion among other things. Various pages cover a number of topics (e.g., astronomy, arithmetic, history) and these are of extremely good quality.
- ArchimedesÐÐŽÐ ÐÐÐÐЇ treatises are known to have been published in both English and Latin during these periods. However, the Latin edition was not published until around the year 820.
This series consists of three collections, with a third being of lesser quality (for the latter two works there are only five in total). The earliest edition published were from 1653. It is also possible that more work was published in Latin between 1630 and 1673, which is generally accepted. More work on this issue can be found in the Library of Congress Directory. More works on this issue can be viewed in the Archive at the Library of Congress Directory.
- A collection for the use of the English edition. This is probably one of the first editions of this treatise but it was printed in the Latin with additional works.
- This volume was written in Latin. It contained a number of illustrations. The most notable are those of Euclid. Since early times the treatise was in many respects an early treatise and although some of these were published after the introduction of Euclid, many of them also appear in the Latin edition. The book has an outline designating some significant topics. The only reference to Euclid’s works can be found in the Catalogue of Greek Classics.
In general, the treatise is very good, is of high quality (e.g., not difficult to read) and provides many important topics for consideration in studying it, ranging from geometry to
Isaac NewtonIsaac 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