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
[hide]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