Details

A triangle center is said to be even when its barycentric coordinates can be expressed as a function of three variables , , that all occur with even exponents. If the center of a triangle has constant barycentric coordinates, it is called a neutral center (the centroid is the only neutral center). A triangle center is said to be odd if it is neither even nor neutral.

Standard barycentric coordinates of a point with respect to a reference triangle have a sum of 1.

References

[1] A. P. Hatzipolakis, F. van Lamoen, B. Wolk and P. Yiu, "Concurrency of Four Euler Lines," Forum Geometricorum, 1, 2001 pp. 59–68. forumgeom.fau.edu/FG2001volume1/FG200109.pdf.

[2] C. Kimberling. "Encyclopedia of Triangle Centers." (Jul 7, 2023) faculty.evansville.edu/ck6/encyclopedia.