Isometry Groups in Planar Geometry - WildTrig: Intro to Rational Trigonometry - N J Wildberger

Explore isometry groups in planar geometry through this 26-minute video lecture. Delve into Euclidean (blue) geometry and two relativistic geometries (red and green) arising from specific dot products or symmetric bilinear forms. Learn about grounded isometries that fix the origin, and discover how reflections and rotations are defined as grounded isometries in each geometry. Gain insights into this classical topic central to graphics and physics, presented with a unique algebraic approach that avoids infinite operations and transcendental circular functions. Understand the composition of isometries, how to check isometry properties, and examine grounded blue and red isometries in detail.