Simplex: Difference between revisions
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imported>Howard Arvi Hughes m (Cz Live) |
imported>Matt Mahlmann (added wikilinks, categories) |
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A simplex is a mathematical object, analogous a triangle. Every simplex has a dimension, which is a nonnegative integer; an n-simplex means a simplex of dimension n. | A '''simplex''' is a mathematical object, analogous a [[triangle]]. Every simplex has a dimension, which is a nonnegative [[integer]]; an n-simplex means a simplex of dimension n. | ||
# A 0-simplex is just a point. | # A 0-simplex is just a [[point]]. | ||
# A 1-simplex is an interval. | # A 1-simplex is an [[interval]]. | ||
# A 2-simplex is a triangle. | # A 2-simplex is a triangle. | ||
# A 3-simplex is a tetrahedron. | # A 3-simplex is a [[tetrahedron]]. | ||
# The standard n-simplex is the set <math>\Delta_n</math> of points <math>x=(x_0,\dots,x_n)\in [0,1]^n</math> for which <math>\sum_ix_i=1</math>. | # The standard n-simplex is the set <math>\Delta_n</math> of points <math>x=(x_0,\dots,x_n)\in [0,1]^n</math> for which <math>\sum_ix_i=1</math>. | ||
[[Category:CZ Live]] | [[Category:CZ Live]] | ||
[[Category:Mathematics Workgroup]] | |||
Revision as of 22:57, 17 April 2007
A simplex is a mathematical object, analogous a triangle. Every simplex has a dimension, which is a nonnegative integer; an n-simplex means a simplex of dimension n.
- A 0-simplex is just a point.
- A 1-simplex is an interval.
- A 2-simplex is a triangle.
- A 3-simplex is a tetrahedron.
- The standard n-simplex is the set of points for which .
![{\displaystyle x=(x_{0},\dots ,x_{n})\in [0,1]^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b905612427282ef93215c83e4cff97384889bbe3)
