Universal A？ne Triangle Geometry and Four-fold Incenter Symmetry

Sa？etak We develop a generalized triangle geometry, using an arbitrary bilinear form in an a？ne plane over a general ？eld. By introducing standardized coordinates we ？nd canonical forms for some basic centers and lines. Strong concurrencies formed by quadruples of lines from the Incenter hierarchy are investigated, including joins of corresponding Incenters, Gergonne, Nagel, Spieker points, Mittenpunkts and the New points we introduce. The diagrams are taken from relativistic (green) geometry