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A triangle center function (sometimes simply called a center function) is a nonzero function f(a,b,c) that is homogeneous f(ta,tb,tc)=t^nf(a,b,c) (1) bisymmetry in b and c, ...

A triangle center alpha:beta:gamma is called a major triangle center if the triangle center function alpha=f(a,b,c,A,B,C) is a function of angle A alone, and therefore beta ...

The Fuhrmann center Fu is the center of the Fuhrmann circle, given by the midpoint of the line joining the Nagel point and orthocenter (which forms a diameter of the Fuhrmann ...

A triangle center is said to be polynomial iff there is a triangle center function f that is a polynomial in a, b, and c (Kimberling 1998, p. 46).

The perspector of the first Morley triangle with reference triangle DeltaABC is called the second Morley center. Its triangle center function is alpha_(357)=sec(1/3A), which ...

The nine-point center N (sometimes instead denoted F) is the center of the nine-point circle. It has equivalent triangle center functions alpha_5 = cos(B-C) (1) alpha_5 = ...

The point at which the three lines connecting the polygon vertices of perspective triangles (from a point) concur, sometimes also called the homology center, pole, or, in ...

There exists a triangulation point Y for which the triangles BYC, CYA, and AYB have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and ...

The center of a Neuberg circle.

The radical lines of three circles are concurrent in a point known as the radical center (also called the power center). This theorem was originally demonstrated by Monge ...