Euclidean Geometry :: essays research papers

Euclidean GeometryGeometry was thoroughly organized in about 300 BC, when the Greekmathematician Euclid gathered what was cognise at the time, added original work ofhis own, and arranged 465 propositions into 13 books, called Elements. Thebooks covered non only plane and solid geometry but also much of what is now cognise 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 notchanged. In the work facts are not just cataloged but are developed in afashionable way.Even in 300 BC, geometry was recognise to be not just formathematicians. Any genius nooky benefit from the basic learning of geometry, whichare how to follow lines of understandinging, how to say precisely what is intended, andespecially how to constitute basic concepts by following these lines of reasoning.Taking a shape in geometry is beneficial for all students, who will find thatlearning to reason and prove convincingly is necessary for every profession. Itis true that not everyone must prove things, but everyone is exposed 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 bepersuaded in the wrong direction. Geometry provides a simplified universe, wherepoints and lines obey believable rules and where conclusions are easily verified.By first studying how to reason in this simplified universe, people caneventually, through practice and experience, learn how to reason in acomplicated world.Geometry in ancient times was recognized as part of everyones education.Early Greek philosophers asked that no one come to their schools who had notlearned the Elements of Euclid. There were, and still are, many who resistedthis kind of education. It is said that Ptolemy I asked Euclid for an easier way