The Life And Work Of Euclid

The Life And Work Of EuclidWhile chartering geometry with Euclid a y egressh inquired after having learned the first advise, What do I get by learning these things? Euclid called a slave to them and said, Give him threepence, since he must make a gain out of what he learns. 8Euclid, a Greek mathematician and teacher, changed the course of the world. Euclids civilise not only affected the black market of other prominent scientists to come after him, al 1 also the lives of medium population, which contri notwithstandinged to the rise of modern science in western civilization. What is perplexing is that scorn him changing the course of world, we know very slender about him. irrelevant some other well-know historical figures, Euclids influence did not dispense simply by fame. Historians dont so far know his exact date of birth. To this sidereal solar day, we do not know which continent he was born on, much slight the city. Of the little we do know about Euclid, we know tha t he taught in Alexandria around 300 B.C. 9, and that he wrote, amongst approximately 10 other haves, arguably one of the greatest mathematical textbooks in archives, The Elements.The Elements is a geometry textbook that incorporated all of the previously known principles of geometry. It was unique in that it was constructive in its actors line of its principles. Basically, it explained mathematic principles from the ground up and added onto what was already established. Imagine trying to study science if one concept didnt run into the next and everything was garbled and out of order. The Elements solved this problem through c beful organization and logical pitch of its principles. The Elements wasnt a revolutionary observation or a new and kindle revelation, but kind of a book of brilliant deductive conclude, analysis, and organization. The Elements was explained so well that every Geometry textbook preceding it was practically discarded, and beca commit of this the term euclidean wasnt necessary or employ for over two thousand historic period because in that location was no other known make of geometry17.Concerning Euclids deductive reasoning and analysis, his axiomatic systems are most prominent. His axiomatic systems are considered to be constructive. 18 This direction that he never clenched whatsoever conclusions or spoke about concepts that he did not yet explain to the reader. He arranged the geometrical theorems so that they flowed logically from one to the next. 9 For example, he started with the simplest of concepts such as describing a geometric point and worked his way into derived propositions. 16 More specifically he took a piddling tot up of axioms (self-evident logical truths) and deduced m whatever other theorems from them. He even fill up in the blanks whenever it was necessary by filling in the missing travel absent from others processes, and even by developing his own proofs 9. For example, Euclid put forwardd that it is unworkable to fall out the largest original number. He proved that if you were to take the largest known prime number and 1 to the product of all the prime numbers pool leading(p) up to it and including it then you will get another prime number. This is authoritative as being one of the classics proofs in math because of how clear and brief it is. 5Euclid put a lot of effort into make it possible for unwashed people to understand geometry rather than secure professional mathematicians. How the natural flow and style of explanation of The Elements affected the world is self-evident. Since it is easier to understand scientific concepts when they are communicated clearly and concisely and delivered in a logical order, Euclids book do it much easier for the people to acquire a complete understanding of geometry. As newborns in this world often one of the first things we get to dally with are blocks of different geometric put to works. This helps us to develop our minds both visually and mathematically. Euclidean shapes are quite literally everywhere in our society. inappropriate Calculus where there is usually a fixed rule for closure a given problem, when it comes to geometry, using Euclidean axioms allows people to solve any one problem in several different ways. It also inspires using of problem solving skills.One of the ways Euclidean geometry has been applied and influences our day to day lives is through winding and architecture. For example, if somebody wants to construct a woody table. If they wanted to figure out if it was square or not they could bar each corner of the table to see if it was at a 90 angle. With Euclidean Geometry, however, they would need only to measure two of the corners. The properties of right triangles deep down The Elements tells us that if two corners are square then the whole shape is square. This is probably very obvious to a person of our modern day, but it was not at the tme. Unless you are a mathemat ician you may not even know who such properties brook be attributed to and just consider them unwashed intimacy. Another, less obvious way they could beat done this is to have calculated the distance between two diagonal corners of the table. If the two distances are the equivalent then the table must be a square. The latter method I have described is a common way for construction workers or home-improvement workers to check their work. There are countless examples of this that common people deal utilize in their everyday lives with the principles of Euclidean Geometry. Euclids influence doesnt bar there. Examples of Euclidean geometry can be shew in modern day computer graphics. It is employ in mesh generation. A mesh is fundamentally a combination of geometric polygons or polyhedrons that create the illusion of a curve. Although the Euclidean Geometry may be widespread within western civilization, in some third world countries there are houses are constructed as lop-side d indeterminate shapes. This is a real-life example of what our architecture would have looked like without Euclids influence.4It is bazar to say that the study of Euclids book was one of the main contributing factors to the scientific Revolution and subsequently the rise of science in Europe rather than in Asia. The Elements do the concept of one principle being built upon another glaringly obvious and, over the course of sentence, it became considered common knowledge in western civilization. Of course, scientists such as due north, Copernicus, Kepler, and Galileo p recumbed significant roles as well 9, but as Sir Isaac Newton said If I have seen further it is by standing on the shoulders of giants 21. Euclids book provided for us, not just a shoulder, but an entire foundation built of giants shoulders that would have other than been scattered and disorganized. This solid base of knowledge allowed western civilization to reach new heights. For example, when it came to Isaac N ewton and his book, Principles Of Natural Philosophy, many of his proofs were set in a geometric cast of characters similar to those found in The Elements. 12As it is with any great work of science, The Elements allows others to build upon it or advance into new areas of discovery. nearly men, such as Girolamo Saccehri, have tried to disprove or find flaws in Euclids axioms. Saccehri was an Italian mathematician who in 1733 nigh discovered a form of non-Euclidean geometry. He studied for eld to find a flaw in Euclids work. He was suppositiously on the verge of a breakthrough but gave up before his work came to fruition. It wasnt until about a hundred years later in 1899 that a German mathematician by the name of David Hilbert found another set of geometric axioms that differed from Euclid. 13 Non-Euclidean geometry allows us to describe physical office in new ways. Following Hilbert came another German, by the name of Albert star. Einstein recalls receiving two gifts that had particular influence on him as a child, one a magnetic compass, and the other Euclids The Elements. He referred to The Elements as the holy little geometry book. 3Another example of a great scientist that was influenced by Euclid is Galileo Galilei. In his octogenarian age Galileo told his biographers that while attendance the University of Pisa he would nose-drop in on lectures being given by Ostilio Ricci to the hook pageboys on Euclid. These lectures were only available to members of the court so he would try to stay quiet whenever he attend them. His interest in Euclid got the better of him after a while and he approached Ricci to ask him questions on Euclid. Ricci noticed Galileos talent for math and eventually became his teacher. Although Galileo was supposed to be going to college to study medicine, (Galen) he secretly studied mathematics (Euclid) instead. Galileo later used Euclids Book Five, Definition Five, to show how bodies of definite exacting weight have weight s directly proportional to their volumes. 2 This is one of the best examples how important Euclids work was to anybody with a mind for mathematics and how he changed the course of history by capturing the interest of a man such as Galileo.Euclids work also influenced philosophers such as Benedict Spinoza. Benedict Spinoza was a prominent philosopher of seventeenth atomic number 6. He wrote the ambitious philosophicical book Ethics where he attempts to provide us with a coherent view of the universe and our fructify in it. To explain such concepts he used Euclids style of delivery complete with axioms and propositions. Speaking of the system within his book and the style in which he chose to present it in Spinoza said that it was designated in geometrical order. 23 Usually philosophical books were pen differently, such as Rene Descartes Meditations that was write like a diary.When it comes to mathematicians I think every mathematician alive since the time of Euclid had to have been influenced by his work in some form or another, but, of some of the most prominent mathematicians, Euclid specifically influenced the work of Bertrand Rusell, Alred North Whitehead, Blaise Pascal, Marin Mersenne , and Adrien-Marie Legendre. interestingly enough Bertrand Russell, an English 20th century mathematician and logician, used Euclids work to charge mathematics into the next level by explaining to people in his book An Essay On The Foundations Of Geometry 11 how Euclidean Geometry was being replaced by more travel forms of geometry. Both Russell and Whitehead were co-authored the epoch Principia Mathmatica in which they referenced Euclid a number of times as evidence in their work. Pascal, a 17th century French mathematician, received a replica of Euclids Elements as a boy and before the age of 13 he had proven the 32nd proposition of Euclid and discovered a flaw in Rene Descartes geometry 25. Mersenne, also a 17th century French mathematician, used Euclids proof on prime numbers to develop his own ways or forms as they are called, making it even easier to find large prime numbers. Prime numbers are important to modern day society because they are used in cryptographic software security systems. Basically, large prime numbers can be implemented into coding schemes that are difficult to break. Legendre, a nineteenth century French mathematician, wrote his most famous book Elments de Gomtrie based entirely off of The Elements. In it he sought to simplify Euclids propositions even further. Elments de Gomtrie was used in elementary take aim classrooms for over a 100 years. 13246Euclid influenced politicians such as Abraham Lincoln. Lincoln, as a lawyer traveling on horse dressing would carry a copy of Euclids Elements in his saddlebag. According to his law partner, at night Lincoln would lay on the floor for hours at night studying Euclids Elements by lamplight. 5 He was a great admirer of the logical delivery of information that The Elements con tained and used Euclids systematic approach in many of his speeches. It is no coincidence that the accent dedicated to the proposition bears such striking similarities to Euclids axioms. Lincoln, speaking of his study of Euclid, said,In the course of my law reading I constantly came upon the word demonstrate. I thought at first that I quiesce its meaning, but presently became satisfied that I did not. I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof?I consulted Websters Dictionary. They told of certain proof, proof beyond the possibility of doubt but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understood demonstration to be. I consulted all the dictionaries and books of reference I could find, but with no better results. You might as well have defined muddy to a blind man.At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means and I left my situation in Springfield, went home to my fathers house, and stayed there till I could give any proposition in the cardinal books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies. 15The astronomers Johannes Kepler and Nicolaus Copernicus were also influenced by Euclids work. When it came to Keplers approach to astronomy he depended almost entirely on Euclid. Kepler, much like Galileo studied Euclid while attending a university (Tbingen). Kepler was a devout Lutheran and considered Euclid geometry to be the only geometry that could be applied to the heavens and refused to use any other form of geometry because he considered such forms to be heretical. He developed a proof of concerning meandering(a) motion based entirely off propositions found in The Elements 22. Copernicus used Euclids work on optics as evidence in his book On The Revolutions Of The Celestial Spheres which was considered the starting point of modern astronomy and the defining epiphany that began the scientific revolution.All these great men of science were not able to use Euclids work as evidence simply because he was well known or famous for doing something exciting and spectacular. It was the intellectual quality of Euclids work that made the difference. We dont know enough about Euclid to either love him nor hate him and unless you pass away to be a mathematician, his work is undoubtedly not awe inspiring. Nevertheless, Euclid still managed to affect some of the most important figures of the Scientific Revolution by setting the foundations necessary for the development of modern science.Sources1. The Lincoln year book, create verbally by Abraham Lincoln, 1809-1865, passage 322. Galileo at Work His Scientific Biography, written by Stillman Drake, pages 2-33. Einstein as a Student, written by Dudley H erschbach, page 34. How To Use Euclidean Geometry, written by Henri Bauholz, http//www.ehow.com/how_4461018_use-euclidean-geometry.html5. Euclid, Math impolite Reference, http//www.mathopenref.com/euclid.html6. groovy Scientists from Euclid to Stephen Hawking, written by John Farndon, 20077. A Chronicle of mathematical People, written by Robert A. Nowlan8. Geometry Quotes, History of Mathematics Archive, http//www-history.mcs.st-and.ac.uk/john/MT4521/Lectures/Q1.html9. The 100 A Ranking Of The Most Influential Persons In History, written by Michael H. Hart, 200010. encyclopaedia of World Biography. Euclid11. The Teaching of Euclid, written by Bertrand Russell, http//www-history.mcs.st-and.ac.uk/Extras/Russell_Euclid.html12. Isaac Newton, Wikipedia, http//en.wikipedia.org/wiki/Isaac_Newton13. Mathematicians Are People, Too Stories from the Lives of Great Mathematicians, written by Luetta Reimer Wilbert Reimer, 199014. The Beginnings of Western Science The European Scientific cu stoms in Philosophical, Religious, and Institutional Context, Prehistory to A.D. 1450, written by David C. Lindberg, 200815. Mathematics From the experience of Numbers, written by Jan Gulberg, 199616. Euclids Elements, written by D.E. Joyce, http//aleph0.clarku.edu/djoyce/java/elements/elements.html17. Euclid, Wikipedia, http//en.wikipedia.org/wiki/Euclid18. Axiomatic Systems for Geometry, written by George Francis, 200219. The Thirteen Books of the Elements, written by Euclid / Thomas L. Heath20. Mathmatical Thought, University of Arkansas, http//math2033.uark.edu/wiki/index.php/EuclidHYPERLINK http//math2033.uark.edu/wiki/index.php/Euclids_ElementsHYPERLINK http//math2033.uark.edu/wiki/index.php/Euclids_Elementss_Elements21. Newton Understanding the Cosmos, New Horizons, Letter from Isaac Newton to Robert Hooke, 1676, as transcribed by Jean-Pierre Maury, 199222. KEPLERS PLANETARY LAWS, written by A. E. Davis, http//www-history.mcs.st-and.ac.uk/HistTopics/Keplers_laws.html23. Spin oza and Jefferson, The Teaching Community, http//teachingcompany.12.forumer.com/viewtopic.php?t=214724. A History of Mathematics, written by Carl B. Boyer, 198525. The History of Computing Project, Blaise Pascal, http//www.thocp.net/biographies/pascal_blaise.html