Department of Mathematics, Statistics
and Computer Science
Wim Ruitenburg's Fall 2010 MATH 1300-101
Last updated: December 2010
Comments and suggestions: Email wimr@mscs.mu.edu
Book, chapter 11 on symmetry
This book chapter mostly considers rigid motions of the plane.
Examples are
- Reflections (improper).
- Rotations (proper).
- Translations (proper).
- Glide reflections (improper).
Usually we only need a little information about points and lines to uniquely
determine the whole rigid motion.
Symmetries of an object are those rigid motions that move the object back onto
itself.
- When we combine or reverse rigid motions, we again get rigid motions.
- All rigid motions can be built from repeated reflections.
- Translations may be considered rotations about a center lying in a
direction at an infinite distance.
- When given a flat object or a spatial object, we consider what proper and
improper symmetries it has, or how many symmetries it has.
- We consider the collection of symmetries of objects in space.
For example, the cube has 48 symmetries, of which 24 are proper and 24 are
improper.