# Difference between revisions of "Geometry"

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− | '''Geometry''' is the branch of mathematics | + | '''Geometry''' is the branch of [[mathematics]] that deals with properties of [[shape]]s and spatial relationships. It is one of the five most basic branches of [[pure mathematics]], the others being [[algebra]], [[number theory]], [[analysis]], and [[logic]]. Primarily, the subject may be divided into six branches: |

− | [[ | + | |

+ | * [[Euclidean geometry]] studies geometry where the [[parallel postulate]] is valid. This includes [[plane geometry]]. | ||

+ | |||

+ | * [[Non-Euclidean geometry]] studies geometry where the parallel postulate is false. | ||

+ | |||

+ | * [[Differential geometry]] studies properties of smooth shapes called differentiable [[manifolds]] by analyzing their [[curvature]] properties. | ||

+ | |||

+ | * [[Algebraic geometry]] studies properties of shapes defined by [[algebraic]] [[equation]]s (e.g. a [[parabola]]) by making use of the additional structures these objects inherit from their algebraic nature. | ||

+ | |||

+ | * [[Topology]], broadly speaking, studies properties of shapes invariant under [[continuous function]]s. | ||

+ | |||

+ | * [[Geometric measure theory]] studies objects that possess a notion of fractional dimension, such as [[fractal]]s. | ||

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+ | ==See also== | ||

+ | * [[Geometric progression]] | ||

+ | |||

+ | ==External links== | ||

+ | *[http://www.learner.org/interactives/geometry/index.html Interactive Geometry 3D Shapes] Learn about three-dimensional shapes, how to calculate their surface area and volume as well as their mathematical properties. | ||

+ | *[http://www.relativitycalculator.com/Minkowski_special_relativity_geometry.shtml The Geometry of Special Relativity: The Minkowski Space - Time Light Cone ] | ||

+ | [[Category:Geometry]] |

## Latest revision as of 13:23, 13 July 2016

**Geometry** is the branch of mathematics that deals with properties of shapes and spatial relationships. It is one of the five most basic branches of pure mathematics, the others being algebra, number theory, analysis, and logic. Primarily, the subject may be divided into six branches:

- Euclidean geometry studies geometry where the parallel postulate is valid. This includes plane geometry.

- Non-Euclidean geometry studies geometry where the parallel postulate is false.

- Differential geometry studies properties of smooth shapes called differentiable manifolds by analyzing their curvature properties.

- Algebraic geometry studies properties of shapes defined by algebraic equations (e.g. a parabola) by making use of the additional structures these objects inherit from their algebraic nature.

- Topology, broadly speaking, studies properties of shapes invariant under continuous functions.

- Geometric measure theory studies objects that possess a notion of fractional dimension, such as fractals.

## See also

## External links

- Interactive Geometry 3D Shapes Learn about three-dimensional shapes, how to calculate their surface area and volume as well as their mathematical properties.
- The Geometry of Special Relativity: The Minkowski Space - Time Light Cone