The Geometry of Euclidean Reflections and Rotations - Grounded Case

Explore the geometry of Euclidean reflections and rotations in this 24-minute video lecture from the Insights into Mathematics series. Delve into a rational approach to understanding these transformations without relying on transcendental functions. Learn how to combine the algebra of reflections and rotations in the "grounded" case, where the origin remains fixed. Discover connections to complex number multiplication, the group structure on the circle, and elementary affine geometry. Examine an interesting insight by F. Lemmermeyer on group structures on general conics. Gain familiarity with a new notation for quickly describing grounded reflections and rotations visually. Topics covered include theorem presentation, conjugates, products of reflections and rotations, the group of blue grounded isometries, and diagram notation.

Introduction
Theorem
An observation by Frank Lemmermeyer
Conjugates
Products of reflections and rotations
The group of blue grounded isometries
Diagram notation