Euclidean Geometry Essays

A line is said to be “a breadthless length”, and a straight line to be a line “which lies evenly with the points on itself”.

This may help convince readers that they share a common conception of the straight line, but it is no use if unexpected difficulties arise in the creation of a theory—as we shall see.

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.

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.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.Projective geometry can be thought of as a deepening of the non-metrical and formal sides of Euclidean geometry; non-Euclidean geometry as a challenge to its metrical aspects and implications.By the opening years of the 20 century a variety of Riemannian differential geometries had been proposed, which made rigorous sense of non-Euclidean geometry.Euclid enters history as one of the greatest of all mathematicians and he is often referred to as the father of geometry.The standard geometry most of us learned in school is called Euclidian Geometry.You can use it freely (with some kind of link), and we're also okay with people reprinting in publications like books, blogs, newsletters, course-material, papers, wikipedia and presentations (with clear attribution).Geometrical knowledge typically concerns two kinds of things: theoretical or abstract knowledge contained in the definitions, theorems, and proofs in a system of geometry; and some knowledge of the external world, such as is expressed in terms taken from a system of geometry.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.