Paper On Euclidean Geometry

528 words - 3 pages

Check the wording and make sure there arnt words you wouldnt use, its about 2 pages or so He liked it a lot.Said it had many good pointsEUCLIDEAN GEOMETRYGeometry was thoroughly organized in about 300 BC, when the Greekmathematician Euclid gathered what was known at the time, added original work of hisown, and arranged 465 propositions into 13 books, called 'Elements'. The books coverednot only plane and solid geometry but also much of what is now known as algebra,trigonometry, and advanced arithmetic.Through the ages, the propositions have been rearranged, and many of theproofs are different, but the basic idea presented in the 'Elements' has not changed. In thework facts are not just cataloged but are developed in a fashionable way.Even in 300 BC, geometry was recognized to be not just for mathematicians.Anyone can benefit from the basic learning of geometry, which are how to follow lines ofreasoning, how to say precisely what is intended, and especially how to prove basicconcepts by following these lines of reasoning. Taking a course in geometry is beneficialfor all students, who will find that learning to reason and prove convincingly is necessaryfor every profession. It is true that not everyone must prove things, but everyone isexposed to proof. Politicians, advertisers, and many other people try to offer convincingarguments. Anyone who cannot tell a good proof from a bad one may easily be persuadedin the wrong direction. Geometry provides a simplified universe, where points and linesobey believable rules and where conclusions are easily verified. By first studying how toreason in this simplified universe, people can eventually, through practice andexperience, learn how to reason in a complicated world.Geometry in ancient times was recognized as part of everyone's education. EarlyGreek philosophers asked that no one come to their schools who had not learned the'Elements' of Euclid. There were, and still are, many who resisted this kind of education.It is said that Ptolemy I asked Euclid for an easier way to learn the material. Euclid toldhim there was no 'royal road' to geometry instead he told Ptolemy you will not learnwhat geometry is all about. What you will learn is the basic shapes of some of the figuresdealt with in geometry and a few facts about them. It takes a geometry course, withtextbook and teacher, to show the complete and orderly arrangement of the facts and howeach is proved.

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