Penrose Tiling

By Joshua John Clark, Daniel Kerstiens, Jason Piercy, and Caleb Rouleau

Outline:

Overview of Penrose Tiling Example: Artist: Urs Schmid Photo by: Urs Schmid Date: drawn in 1995

Who is Roger Penrose?

 1. Oxford professor
 2. PhD from Cambridge

Definition of non-periodic

(http://en.wikipedia.org/wiki/Non-periodic)

Types of Penrose Tilings

  1. Original Pentagonal
  2. Kite and Dart
  3. Rhombus

Symmetries: local and global

  1. Rotational 
  2. Reflectional 
  3. Relation to golden ratio

Rules for construction

  1. Matching rules
  2. Substitution tiling

Other tilings

References

Gallian, J. (2013). Contemporary abstract algebra. (8th ed.). Boston, MA: Brooks/Cole, Cengage Learning. http://www.ics.uci.edu/~eppstein/junkyard/tiling