References for Euclid and other geometries

• Euclid's Elements, Greek original and side by side English translation by Richard Fitzpatrick.

  • All 13 books, from the web farside.ph.utexas.edu/euclid/elements.pdf

  • A local copy

  • Book 1 (48 pages)

  • From Amazon for a paltry $25!

• A nice on line easy to read annotated version, with Java applets for the diagrams: aleph0.clarku.edu/~djoyce/java/elements/

• Dover has reprinted The classic Heath edition Vol I, Books 1 and 2, for just $16. It's even a little less at Amazon.

• Proofs that the Pythagorean Theorem and the Theorem on the sum of the angles of a triangle (and several other theorems) each imply the parallel postulate: www.cut-the-knot.org/triangle/pythpar/PTimpliesPP.shtml

• Postulates for Lobachevsky-Bolyai geometry: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1078171/pdf/pnas01615-0055.pdf

• Math and the Art of M. C. Escher - euler.slu.edu/escher/index.php/Math_and_the_Art_of_M._C._Escher

• Tiling the hyperbolic plane.
  • wikipedia.org/wiki/Uniform_tilings_in_hyperbolic_plane
  • euler.slu.edu/escher/index.php/Circle_Limit_Exploration
  • M.C. Escher and Hyperbolic Geometry www.math.cornell.edu/~mec/Winter2009/Mihai/
  Crochet: www.theiff.org/oexhibits/oe1e.html