Anticomplement
The anticomplement of a point P in a reference triangle DeltaABC is a point P^' satisfying the vector equation
| P^'G^->=2GP^->, |
(1)
|
where G is the triangle centroid of DeltaABC (Kimberling 1998, p. 150).
The anticomplement of a point with center function alpha:beta:gamma is therefore given by the point with trilinears
The anticomplement of a line
| lalpha+mbeta+ngamma=0 |
(3)
|
is given by the line
| a^2(cm+bn)alpha+b^2(cl+an)beta+c^2(bl+am)gamma=0. |
(4)
|
The following table summarizes the anticomplements of a number of named lines, including their Kimberling line and center designations.
The following table summarizes the anticomplements of a number of named circles.
The following table lists some points and their anticomplements using Kimberling center designations.
See also
ComplementExplore with Wolfram|Alpha
More things to try:
References
Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Referenced on Wolfram|Alpha
AnticomplementCite this as:
Weisstein, Eric W. "Anticomplement." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Anticomplement.html