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]]''. | ||
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| + | ===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 == | ||
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== See also == | == See also == | ||
| − | |||
* [[Mathematics news]] | * [[Mathematics news]] | ||
| + | * [[The Elements]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 22:21, 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
