  We prove that for any point set P in the plane, a triangle T, and a positive
integer k, there exists a coloring of P with k colors such that any homothetic
copy of T containing at least ck^8 points of P, for some constant c, contains
at least one of each color. This is the first polynomial bound for range spaces
induced by homothetic polygons. The only previously known bound for this
problem applies to the more general case of octants in R^3, but is doubly
exponential.
