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# Triangle Cubic

A triangle cubic is a curve that can be expressed in trilinear coordinates such that the highest degree term in the trilinears , , and is of order three.

Wells (1991) describes a cubic curve on which 37 notable triangle centers lie. Other triangle cubics include the M'Cay cubic (Gallatly 1913, p. 80) and Thomson cubic (Kimberling 1998, p. 240).

Brocard Cubic, Darboux Cubic, Droussent Cubic, Isocubic, Lemoine Cubic, Lucas Cubic, M'Cay Cubic, Napoleon-Feuerbach Cubic, Neuberg Cubic, Orthocubic, Pivotal Isocubic, Pivotal Isogonal Cubic, Pivotal Isotomic Cubic, Self-Isogonal Cubic, Simson Cubic, Thomson Cubic, Tucker-Brocard Cubic, Tucker Cubic

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## References

Cundy, H. M. and Parry, C. F. "Some Cubic Curves Associated with a Triangle." J. Geom. 53, 41-66, 1995.Gallatly, W. The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, 1913.Gibert, B. "Cubics in the Triangle Plane." http://perso.wanadoo.fr/bernard.gibert/.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Rubio, P. "Cubic Lines Relative to a Triangle." J. Geom. 34, 152-171, 1989.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 42-43, 1991.Yff, P. "Two Families of Cubics Associated with a Triangle." In MAA Notes, No. 34. Washington, DC: Math. Assoc. Amer., 1994.

Triangle Cubic

## Cite this as:

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