Reference Triangle

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 DeltaABC, its excentral triangle, then its tangential triangle," DeltaABC 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 A-vertex are 1:0:0, the coordinates of the B-vertex are 0:1:0, and the coordinates of the C-vertex are 0:0:1.

See also

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References

Referenced on Wolfram|Alpha

Cite this as:

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

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