Tiling with a Pocket-Sized xy-Plane

One area of recreational reserach of mine is investigating the symmetries of point sets in the plane (eg. graphs of functions) under a particular transformation which maps the entire real line onto an open interval of length 4. 

In January of 2006, I presented some preliminary findings in a Math Club talk. Below I include the talk announcement and abstract, originals of the transparencies that I sketched upon during the talk, and (page by page) the images that I sketched during the talk.

Please contact me if you find this interesting and would like to share in the investigation!

Announcement and Abstract

 (Word file)

Completed Color Transparencies (all jpeg files)
  • - Welcome
  •  - Introduce the compression
  •  - Graphing in the compressed plane
  •  - Graphs of pure power functions
  •  - Sources of Symmetry
  • - Symmetry Examples
  • - Tiling in the Compressed Plane
  • - More Tiling
  • - Differentiation in the Compressed Plane
  • - More Differentiation
  • - Concavity in the Compressed Plane
  • - More Concavity
  • - Further Study
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