Isometry groups in planar geometry | WildTrig: Intro to Rational Trigonometry | N J Wildberger

In this video we look at isometry groups in three planar geometries, the Euclidean (blue) geometry, and two relativistic geometries (red and green). These geometries arise from particular dot products, or symmetric bilinear forms.

To simplify the discussion, we first introduce grounded isometries which fix the origin. Then in each of these geometries we can define reflections and rotations as grounded isometries.

While this is a classical topic which lies at the heart of a lot of graphics and physics, our treatment is necessarily quite different form the usual, as we are not allowing ourselves the indulgence of contemplating infinite operations, in other words angles and transcendental circular functions. We need to be more careful and algebraic!

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