Triangle (EntityTopic, 17)

From Hi.gher. Space

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| pv_circle=<sup>[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>π</sub> ≈ 0.2757
| pv_circle=<sup>[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>π</sub> ≈ 0.2757
| pv_square=[[Sine values|S<sub>1</sub>]]+S<sub>1</sub><sup>3</sup>S<sub>5</sub><sup>-2</sup> ≈ 0.2774
| pv_square=[[Sine values|S<sub>1</sub>]]+S<sub>1</sub><sup>3</sup>S<sub>5</sub><sup>-2</sup> ≈ 0.2774
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| extra={{STS Matrix|
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3 0
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1 1}}{{STS Rotope
| attrib=pure
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| notation=1<sup>1</sup> x<sup>y</sup>
| notation=1<sup>1</sup> x<sup>y</sup>

Revision as of 00:40, 8 November 2008


A triangle is a two-dimensional simplex.

The triangle is important as all polygons can be defined as the union of a set of triangles joined edge to edge, and all polytopes in greater than two dimensions can be defined as the hypervolume bounded by the union of a set of triangles.

Equations

  • The area of an arbitrary triangle is:
absin(C)2-1
  • where a and b are two sides of the triangle and C is the angle between them.

Segmentation

The equilateral triangle of side 1 may be segmented into 3× triangle with sides 1, 2×3-2-1 and angles 2×30°, 120°.

Use

Triangular faces are found in these trishapes on FGwiki:

Triangular segments are found in these dishapes on FGwiki:


Notable Dishapes
Flat: trianglesquarepentagonhexagonoctagondecagon
Curved: circle

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