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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


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

Kimberling, C. ``Triangle Centers.''

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

© 1996-9 Eric W. Weisstein