# Difference between revisions of "Geometry"

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− | '''Geometry''' is the field of [[mathematics]] dealing with figures in a given space. | + | '''Geometry''' is the field of [[mathematics]] dealing with figures in a given space. |

+ | == Euclidean Geometry == | ||

+ | {{main|Euclidean geometry}} | ||

+ | The most common type of geometry used in pre-[[college|collegiate]] [[mathematics competitions]] is Euclidean geometry. This type of geometry was first formally outlined by the Greek [[mathematician]] [[Euclid]] in his book ''[[The Elements]]''. | ||

+ | |||

+ | ===Eleventh Postulate=== | ||

+ | {{main|The Eleventh Postulate}} | ||

+ | The eleventh [[postulate]] stated in the book, | ||

+ | |||

+ | :''“Through any line and a point not on the line, there is exactly one line passing through that point parallel to the line”'' | ||

+ | |||

+ | was the subject of a controversy for many centuries. This postulate is the basis of Euclidean geometry. | ||

+ | |||

+ | == Non-Euclidean Geometry == | ||

+ | Non-Euclidean geometry are geometries in which the eleventh postulate is altered. Types of non-Euclidean geometry include: | ||

+ | *[[Elliptical geometry]] | ||

+ | *[[Hyperbolic geometry]] | ||

== Student Guides to Geometry == | == Student Guides to Geometry == | ||

Line 13: | Line 29: | ||

== See also == | == See also == | ||

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* [[Mathematics news]] | * [[Mathematics news]] | ||

+ | * [[The Elements]] | ||

[[Category:Geometry]] | [[Category:Geometry]] |

## Revision as of 21:21, 3 December 2007

**Geometry** is the field of mathematics dealing with figures in a given space.

## Contents

## Euclidean Geometry

*Main article: Euclidean geometry*

The most common type of geometry used in pre-collegiate mathematics competitions is Euclidean geometry. This type of geometry was first formally outlined by the Greek mathematician Euclid in his book *The Elements*.

### Eleventh Postulate

*Main article: The Eleventh Postulate*

The eleventh postulate stated in the book,

*“Through any line and a point not on the line, there is exactly one line passing through that point parallel to the line”*

was the subject of a controversy for many centuries. This postulate is the basis of Euclidean geometry.

## Non-Euclidean Geometry

Non-Euclidean geometry are geometries in which the eleventh postulate is altered. Types of non-Euclidean geometry include:

## Student Guides to Geometry

## Other Topics of Interest

- The notion of dimensions