Chromogeometry

Abstract

Chromogeometry brings together Euclidean geometry (called blue) and two relativistic geometries (called red and green), in a surprising three-fold symmetry. We show how the red and green `Euler lines' and `nine-point circles' of a triangle interact with the usual blue ones, and how the three orthocenters form an associated triangle with interesting collinearities. This is developed in the framework of rational trigonometry using quadrance and spread instead of distance and angle. The former are more suitable for relativistic geometries.