Triangle Center Function

A Homogeneous Function $f(a, b, c)$, i.e., a function $f$ such that

$$f(ta, tb, tc) = t^n f(a, b, c),$$

which gives the Trilinear Coordinates of a Triangle Center as

$$\alpha:\beta:\gamma = f(a, b, c):f(b, c, a):f(c, a, b).$$

The variables may correspond to angles ($A$, $B$, $C$) or side lengths ($a$, $b$, $c$), since these can be interconverted using the Law of Cosines.

See also Major Triangle Center, Regular Triangle Center, Triangle Center, Trilinear Coordinates

References

Kimberling, C. ``Triangle Centers as Functions.'' Rocky Mtn. J. Math. 23, 1269-1286, 1993.

Kimberling, C. ``Triangle Centers.'' http://cedar.evansville.edu/~ck6/tcenters/.

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