A family of geometric operators on triangles with two complex variables

Abstract

Given a plane triangle $\Delta$, one can construct a new triangle ${\Delta }^{\prime }$ whose vertices are intersections of two cevian triples of $\Delta$. We extend the family of operators $\Delta \mapsto {\Delta }^{\prime }$ by complexifying the defining two cevian parameters and study its rich structure from arithmetic-geometric viewpoints. We also find another useful parametrization of the operator family via finite Fourier analysis and apply it to investigate area-preserving operators on triangles.

Journal of Geometry