Rational Trigonometry, Generalized Triangle Geometry and Four-Fold Incenter Symmetry

Explore a seminar talk on rational trigonometry and generalized triangle geometry, delving into an algebraic approach that replaces traditional concepts with quadrances and spreads. Learn about the application of rational trigonometry to relativistic geometry and chromogeometry. Discover a general approach to triangle geometry using linear transformations and standard triangles. Examine the incenter hierarchy, its four-fold symmetry, and interesting concurrences associated with various triangle centers. Investigate the blue, red, and green Pythagoras theorems, Euler lines, and incenter circles. Gain insights into bilines, Gergonne points, Nagel points, and Mittenpunkts. Uncover the connections between different geometric concepts and their applications in this comprehensive exploration of advanced trigonometry and triangle geometry.