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"Out of nothing I have created a strange new universe. "
Janos Bolyai, on the creation of a non-Euclidean geometry


Geometry

Geometry

[Gr., = earth measuring],
Branch of mathematics
concerned with the properties of and relationships between
points, lines, planes, and figures
and with generalizations of these concepts.


History:

In 1637, Rene Descartes showed how numbers can be used to describe points in a plane or in space and to express geometric relations in algebraic form, thus founding analytic geometry , of which algebraic geometry is a further development. The problem of representing three-dimentional object on a two-dimensional surgace was solved by Gaspard Monge, who invented descriptive geometry for this purpose in the late 18th cent. differential geometry , in which the concepts of the calculus are applied to curves, surfaces, and other geometrical objects, was founded by Monge and C. F . Gauss in the late 18th and early 19th cent. The modern period in geometry begins with the formulatins of projective geometry by J. V. Poncelet (1822) and of non-Euclidean geometry by N. I . Lobachevsky (1826) and Janos Bolyai (1832). Another type of non-Euclidean geometry was discovered by Georg Riemann (1854), who also showed how the various geometries could be generalized to any number of dimensions.

Simple Basic concept:

Points 
|--> Lines
|--> Planes
|--> Space

Links:

Math Forum
College-Level Geometry

Introduction to Geometry

An introduction toProjective Geometry (for computer vision)

 

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