Difference between revisions of "Geometry"
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| − | '''Geometry''' is the branch of mathematics that deals with properties of [[shape]]s and spatial relationships | + | '''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. | * [[Euclidean geometry]] studies geometry where the [[parallel postulate]] is valid. | ||
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* [[Topology]], broadly speaking, studies properties of shapes invariant under [[continuous function]]s. | * [[Topology]], broadly speaking, studies properties of shapes invariant under [[continuous function]]s. | ||
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| + | * [[Geometric measure theory]] studies objects that possess a notion of fractional dimension, such as fractals. | ||
[[category:geometry]] | [[category:geometry]] | ||
Revision as of 19:23, June 30, 2008
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.
- 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, 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.
