Triangle (EntityTopic, 17)
From Hi.gher. Space
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<blockquote>''ab''sin(''C'')2<sup>-1</sup></blockquote> | <blockquote>''ab''sin(''C'')2<sup>-1</sup></blockquote> | ||
*where ''a'' and ''b'' are two sides of the triangle and ''C'' is the angle between them. | *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 [[segment]]ed into 3× triangle with sides 1, 2×3<sup>-2<sup>-1</sup></sup> and angles 2×30°, 120°. | ||
{{Dishapes}} | {{Dishapes}} | ||
{{Rotope Nav|2|3|4|II<br>Square|I'<br>Triangle|(II)<br>Circle|gons}} | {{Rotope Nav|2|3|4|II<br>Square|I'<br>Triangle|(II)<br>Circle|gons}} | ||
Revision as of 16:45, 16 September 2007
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, and all polytopes in greater than two dimensions can be defined as the hypervolume bounded by the union of a set of triangles.
Geometry
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°.
| Notable Dishapes | |
| Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
| Curved: | circle |
