**"Out of nothing I have created a strange new universe."**

*Janos Bolyai, on the creation of a non-Euclidean geometry*

# Geometry

*{gr.,=earth measuring},*

Branch of mathematice

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 geopetry is a further development. The problem of
reresenting three-dimensional objects on a two-dimensional surface 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 found by
Monge and C.F. Gauss in the late 19th and early 19th cent. The modern period
in geometry begins with the formulations 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 geometrics could be generalized to any
number of dimensions.

## Simple Basic Concept:

Points

|--> Lines

|--> Planes

|--> Space

## Links:

College-Level Geometry

Introduction
to Geometry

An Introduction to
Projective Geometry (for computer vision)

:

## Comments:

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