simplex - Definition. Was ist simplex
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Was (wer) ist simplex - definition

GENERALIZATION OF THE NOTION OF A TRIANGLE OR TETRAHEDRON TO ARBITRARY DIMENSIONS
Simplices; Affine simplex; Affine chain; Singular simplex; Simplex (mathematics); Simplicial; Simplex (abstract); Unit simplex; Standard simplex; Singular n-simplex; 2-simplex; Hypertriangle; N-simplex; 11-simplex; 12-simplex; 15-simplex; 14-simplex; 13-simplex; 16-simplex; 17-simplex; 18-simplex; 19-simplex; Euclidean simplex; 20-simplex; Simplex (geometry); Singular simplices functor; Regular simplex; Face of a simplex
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  • The numbers of faces in the above table are the same as in [[Pascal's triangle]], without the left diagonal.
  • The four simplexes which can be fully represented in 3D space.
  • The total number of faces is always a [[power of two]] minus one.  This figure (a projection of the [[tesseract]]) shows the centroids of the 15 faces of the tetrahedron.

simplex         
1. <communications> Used to describe a communications channel that can only ever carry a signal in one direction, like a one-way street. Television is an example of (broadcast) simplex communication. Opposite: duplex. 2. <algorithm> The simplex method. (2001-07-21)
simplex         
¦ adjective technical
1. composed of or characterized by a single part or structure.
2. (of a communication system, computer circuit, etc.) only allowing transmission of signals in one direction at a time.
¦ noun a simple or uncompounded word.
Origin
C16: from L., lit. 'single', var. of simplus 'simple'.
Simplex         
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope made with line segments in any given dimension.

Wikipedia

Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example,

  • a 0-dimensional simplex is a point,
  • a 1-dimensional simplex is a line segment,
  • a 2-dimensional simplex is a triangle,
  • a 3-dimensional simplex is a tetrahedron, and
  • a 4-dimensional simplex is a 5-cell.

Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices. More formally, suppose the k + 1 points u 0 , , u k {\displaystyle u_{0},\dots ,u_{k}} are affinely independent, which means that the k vectors u 1 u 0 , , u k u 0 {\displaystyle u_{1}-u_{0},\dots ,u_{k}-u_{0}} are linearly independent. Then, the simplex determined by them is the set of points

A regular simplex is a simplex that is also a regular polytope. A regular k-simplex may be constructed from a regular (k − 1)-simplex by connecting a new vertex to all original vertices by the common edge length.

The standard simplex or probability simplex is the k − 1 dimensional simplex whose vertices are the k standard unit vectors in R k {\displaystyle \mathbb {R} ^{k}} , or in other words

In topology and combinatorics, it is common to "glue together" simplices to form a simplicial complex. The associated combinatorial structure is called an abstract simplicial complex, in which context the word "simplex" simply means any finite set of vertices.

Beispiele aus Textkorpus für simplex
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5. Fifty–three year old Gest is claiming that Miss Minnelli hid herpes simplex, a sexually transmitted infection, from him until after their marriage.