Simplex: Difference between revisions

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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.
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# A 0-simplex is just a point.
A '''simplex''' is a mathematical object, analogous to a [[triangle]]. Every simplex has a dimension, which is a nonnegative [[integer]]; an n-simplex means a simplex of dimension n.
# 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 <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]]
# A 0-simplex is just a [[point]].
# A 1-simplex is an [[interval]] or line segment.
# A 2-simplex is a filled-in triangle.
# A 3-simplex is a solid [[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>.  For example, the standard 3-simplex is the shape of the corner of a cube if it is sliced off at an angle to produce a solid with three similar triangular faces (parts of the sides of the cube) and one larger, equilateral triangular face.

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A simplex is a mathematical object, analogous to a triangle. Every simplex has a dimension, which is a nonnegative integer; an n-simplex means a simplex of dimension n.

  1. A 0-simplex is just a point.
  2. A 1-simplex is an interval or line segment.
  3. A 2-simplex is a filled-in triangle.
  4. A 3-simplex is a solid tetrahedron.
  5. The standard n-simplex is the set of points for which . For example, the standard 3-simplex is the shape of the corner of a cube if it is sliced off at an angle to produce a solid with three similar triangular faces (parts of the sides of the cube) and one larger, equilateral triangular face.
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