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Lemoine Cubic

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LemoineCubic

The Lemoine cubic is the triangle cubic with trilinear equation

2(a^2-b^2)(b^2-c^2)(c^2-a^2)aalphabbetacgamma+sum_(cyclic)a^4(b^2+c^2-a^2)bbetacgamma(bbeta-cgamma)=0.

It passes through Kimberling centers X_n for n=3, 4, 32, 56, and 1147.

See also

Triangle Cubic

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References

Gibert, B. "The Lemoine Cubic and Its Generalizations." Forum Geom. 2, 47-63, 2002. https://web.archive.org/web/20230127212117/https://forumgeom.fau.edu/FG2002volume2/FG200207index.html.Gibert, B. "Lemoine Cubic." http://bernard-gibert.fr/Exemples/k009.html.Lemoine, E. Association Française pour l'Avancement des Sciences. p. 149, 1891.Lemoine, E. Association Française pour l'Avancement des Sciences. p. 124, 1892.

Referenced on Wolfram|Alpha

Lemoine Cubic

Cite this as:

Weisstein, Eric W. "Lemoine Cubic." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LemoineCubic.html

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