Скачать или смотреть Math 533, Fall 2025, Week 8: Rotations

In this video, we do some quick review of earlier topics. We introduce the idea of rotation in Euclidean geometry. The challenge is that our definition of angle is unsigned, i.e. it doesn't tell the difference between counterclockwise and clockwise angles. Our solution is to break down a rotation as a composition of 2 reflections.
(Video 1 of Week 8)

0:00 intro
0:32 review
4:27 intuitive idea of rotation
6:31 problem of signed vs unsigned angles
7:31 proposed solution to problem: composition of 2 reflections
10:29 formal definition of rotation as composition of reflections
11:28 explanation of this description
14:42 homework
15:35 recap of the logic behind our definition