Chromogeometry

Three-fold symmetry is at the heart of a lot of interesting mathematics and physics. Here, Wildberger shows that three-fold symmetry also plays an unexpected role in planar geometry, in that the familiar Euclidean geometry is only one of a trio of interlocking metric geometries. He refers to Euclidean geometry as blue geometry; the other two geometries, called red and green, are relativistic in nature and are associated with the names of Lorentz, Einstein, and Minkowski. In basic structure, all three geometries are similar--they are ruled by the laws of rational trigonometry as developed recently in, which hold over a general field not of characteristic.