Euclidean Geometry Essay, Research Paper

Euclidean Geometry

Geometry was thoroughly organized in about 300 BC, when the Greek

mathematician Euclid gathered what was known at the time, added original work of

his own, and arranged 465 propositions into 13 books, called ‘Elements’. The

books covered not 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 the

proofs are different, but the basic idea presented in the ‘Elements’ has not

changed. In the work 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 of reasoning, how to say precisely what is intended, and

especially how to prove basic concepts by following these lines of reasoning.

Taking a course in geometry is beneficial for all students, who will find that

learning to reason and prove convincingly is necessary for every profession. It

is true that not everyone must prove things, but everyone is exposed to proof.

Politicians, advertisers, and many other people try to offer convincing

arguments. Anyone who cannot tell a good proof from a bad one may easily be

persuaded in the wrong direction. Geometry provides a simplified universe, where

points and lines obey believable rules and where conclusions are easily verified.

By first studying how to reason in this simplified universe, people can

eventually, through practice and experience, learn how to reason in a

complicated world.

Geometry in ancient times was recognized as part of everyone’s education.

Early Greek 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 told him there was no “royal road” to geometry

instead he told Ptolemy you will not learn what geometry is all about. What you

will learn is the basic shapes of some of the figures dealt with in geometry and

a few facts about them. It takes a geometry course, with textbook and teacher,

to show the complete and orderly arrangement of the facts and how each is proved.

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