On Ceva points of (almost) equilateral triangles

Abstract A Ceva point of a rational-sided triangle is any internal or external point such that the lengths of the three cevians through this point are rational. Buchholz [Buc89] studied Ceva points and showed a method to construct new Ceva points from a known one. We prove that almost-equilateral and equilateral rational triangles have infinitely many Ceva points by establishing a correspondence to points in certain elliptic surfaces of positive rank.