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
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Math 370 home page
.