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Reciprocal Conjugation


Let P and U be points, neither of which lies on a sideline of DeltaABC, given in barycentric coordinates by P=p:q:r and U=u:v:w. The P-reciprocal conjugate of U is then the point

 pvw:qwu:ruv

in barycentric coordinates.

The term "reciprocal conjugate" was introduced in Dean and van Lamoen (2001). Confusingly, the term has sometimes also been used to mean isoconjugation.


See also

Isoconjugation

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References

Dean, K. R. and van Lamoen, F. M. "Geometric Construction of Reciprocal Conjugates." Forum Geom. 1, 115-120, 2001. http://forumgeom.fau.edu/FG2001volume1/FG200116index.html.Kimberling, C. "Glossary: A Support Pages for Encyclopedia Triangle Centers." http://faculty.evansville.edu/ck6/encyclopedia/glossary.html.van Lamoen, F. M. "Pl-Perpendicularity." Forum Geom. 1, 151-160, 2001. http://forumgeom.fau.edu/FG2001volume1/FG200122index.html.

Referenced on Wolfram|Alpha

Reciprocal Conjugation

Cite this as:

Weisstein, Eric W. "Reciprocal Conjugation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ReciprocalConjugation.html

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