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).
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.
, 
, and 
is of order three.
