center function

A triangle center function (sometimes simply called a center function) is a nonzero function f(a, b, c) that is homogeneous f(t a, t b, t c) = t^n f(a, b, c) bisymmetry in b and c, f(a, c, b) = f(a, b, c) and such that the trilinear coordinates of the triangle center encoded by the function are cyclic in a, b, and c, α:β:γ = f(a, b, c):f(b, c, a):f(c, a, b).

exact trilinear coordinates | Kimberling center | major triangle center | regular triangle center | triangle center | trilinear coordinates