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A reference triangle is a triangle relative to which trilinear coordinates, exact trilinear coordinates, derived triangle, or other objects are defined in triangle geometry (Kimberling 1998, p. 155).

For example, in the construction "take a triangle , its excentral triangle, then its tangential triangle," is the reference triangle." For example, the orthic triangle is perspective with the reference triangle, with the perspector being the orthocenter. In this context, the reference triangle is also known as the original triangle.

The reference triangle is the polar triangle of the polar circle and Stammler hyperbola.

A reference triangle has trilinear vertex matrix

i.e., the trilinear coordinates of the -vertex are 1:0:0, the coordinates of the -vertex are 0:1:0, and the coordinates of the -vertex are 0:0:1.

See also

Central Triangle, Triangle Geometry, Trilinear Coordinates, Trilinear Vertex Matrix

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References

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

Referenced on Wolfram|Alpha

Reference Triangle

Cite this as:

Weisstein, Eric W. "Reference Triangle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ReferenceTriangle.html

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