Let P=p:q:r and U=u:v:w be points in trilinear coordinates, neither of which is on a side line of a reference triangle DeltaABC. Them the P-isoconjugate of U is the point


Isogonal and isotomic conjugations are examples of isoconjugations.

The earliest appearance of the term "isoconjugate" in triangle geometry may have been by Kimberling as early as 1998. Isoconjugates were also discussed in Kimberling (2001, 2002). Thereafter, the term "isoconjugate" has sometimes been used to mean reciprocal conjugate, which is a different sort of conjugate (Kimberling).

See also

Isogonal Conjugate, Isotomic Conjugate, Reciprocal Conjugation

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Gibert, B. "Isoconjugation.", C. "Glossary: A Support Pages for Encyclopedia Triangle Centers.", C. "Conjugacies in the Plane of a Triangle." Aeq. Math. 63, 158-167, 2000.Kimberling, C. "Conics Associated with Cevian Nest." Forum Geom. 1, 141-150, 2001a., C. "Cubics Associated with Triangles of Equal Areas." Forum Geom. 1, 161-171, 2001b., C. "Conjugacies in the Plane of a Triangle." Aeq. Math. 63, 158-167, 2002.

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Cite this as:

Weisstein, Eric W. "Isoconjugation." From MathWorld--A Wolfram Web Resource.

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