Euclidean Geometry Essays

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Great philosopher mathematicians such as Descartes and Newton presented their philosophical works using Euclid's structure and format, moving from simple first principles to complicated concepts.

Abraham Lincoln was a fan, and the US Declaration of Independence used Euclid's axiomatic system.

To those who decided to read the carefully and see how the crucial terms are used, it became apparent that the account is both remarkably scrupulous in some ways and flawed in others.

Straight lines arise almost always as finite segments that can be indefinitely extended, but, as many commentators noted, although Euclid stated that there is a segment joining any two points he did not explicitly say that this segment is unique.From this basis, he built his entire theory of plane geometry, which has shaped mathematics, science and philosophy for centuries.He proved that it is an impossibility to find the 'largest prime number,' because taking the largest known prime number and adding one to the product of all previous primes and the largest prime will give you another, larger prime number.Euclid probably attended Plato's academy in Athens before moving to Alexandria, in Egypt.At this time, the city had a huge library and the ready availability of papyrus made it the center for books, the major reasons why great minds such as Heron of Alexandria and Euclid based themselves there.Apart from the Elements, Euclid also wrote works about astronomy, mirrors, optics, perspective and music theory, although many of his works are lost to posterity.Certainly, he can go down in history as one of the greatest mathematicians of all time, and he was certainly one of the giants upon whose shoulders Newton stood.He therefore gave a bald claim that one triangle may be copied exactly in an arbitrary position, which makes one wonder why such care was expended on I.2.In fact, the whole concept of motion of figures was to become a prolonged topic of discussion in Arab/Islamic times. A plausible reading of Book I is that a straight line can be understood as having a direction, so that there is a straight line in every direction at every point and only one straight line at a given point in a given direction.Euclid based his approach upon 10 axioms, statements that could be accepted as truths.He called these axioms his 'postulates' and divided them into two groups of five, the first set common to all mathematics, the second specific to geometry.

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