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Unit 8

Geometries Beyond Euclid



Anderson, Michael T. "Scalar Curvature and Geometrization Conjectures for 3-Manifolds," Comparison Geometry, vol. 30 (1997).

Aste, Tomaso. "The Shell Map: The Structure of Froths Through a Dynamic Map." (arXiv:cond-mat/9803183v1), (1998). http://arxiv.org/ (accessed 2007.)

Berlinghoff, William P. and Kerry E. Grant. A Mathematics Sampler: Topics for the Liberal Arts, 3rd ed. New York: Ardsley House Publishers, Inc., 1992.

Boyer, Carl B. (revised by Uta C. Merzbach). A History of Mathematics, 2nd ed. New York: John Wiley and Sons, 1991.

Burton, David M. History of Mathematics: An introduction, 4th ed. USA: WCB/ McGraw-Hill, 1999.

Cannon, James W., William J. Floyd, Richard Kenyon, and Walter R. Parry. "Hyperbolic Geometry," in No. 31 of Mathematical Sciences Research Institute Publications, Flavors of Geometry, edited by Silvio Levy, 59-115. New York: Cambridge University Press, 1997.

Conway, J.H. and S. Torquato, "Packing, Tiling, and Covering with Tetrahedra" Proceedings of the National Academy of Sciences, USA, vol. 103, no. 28. (July 2006).

Coxeter, H.S.M. Non-Euclidean Geometry, 6th ed. Washington, DC: Mathematical Association of America, 1998.

Delman, Charles and Gregory Galperin. "A Tale of Three Circles," Mathematics Magazine, vol. 76, no.1 (February 2003).

Deza, Michel and Mikhail Shtogrin. "Uniform Partitions of 3-Space, Their Relatives and Embedding," European Journal of Combinatorics, vol. 21, no. 6 (August 2000).

Euclid. The Thirteen Books of Euclid's Elements, translated from the text of Heiberg, with introduction and commentary by Sir Thomas L. Heath, 2nd ed. (unabridged). New York: Dover Publications, 1956.

Eves, Howard. An Introduction to the History of Mathematics, 5th ed. (The Saunders Series) Philadelphia, PA: Saunders College Publishing, 1983.

Gauglhofer, Thomas and Hugo Parlier. "Minimal Length of Two Intersecting Simple Closed Geodesics," Manuscripta Mathematica, vol. 122, no. 3 (2007).

Goe, George, B.L. van der Waerden, and Arthur I. Miller. "Comments on Miller's "The Myth of Gauss' Experiment on the Euclidean Nature of Physical Space," Isis, vol. 65, no. 1 (March 1974).

Goodman-Strauss, Chaim. "Compass and Straightedge in the Poincaré Disk," American Mathematical Monthly, vol. 108, no. 1 (January 2001).

Greenberg, Marvin Jay. Euclidean and Non-Euclidean Geometries: Development and History. 2nd ed, New York: W.H. Freeman and Co., 1980.

Greene, Brian. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. New York: W.W. Norton and Co., 1999.

Lederman, Leon M. and Christopher T. Hill. Symmetry and the Beautiful Universe. Amherst, NY: Prometheus Books, 2004.

Luminet, Jean-Pierre and Boudewijn F. Roukema. "Topology of the Universe: Theory and Observations." Cornell University Library. http://fr.arxiv.org/abs/astro-ph/9901364v3 (accessed 2007).

Miller, Arthur I. "The Myth of Gauss' Experiment on the Euclidean Nature of Physical Space," Isis, vol. 63, no. 3 (September 1972).

Monastyrsky, Michael. [Translated by James King and Victoria King. Edited by R.O. Wells Jr.] Riemann, Topology and Physics. Boston, MA: Birkhauser, 1979.

O'Shea, Donal. The Poincaré Conjecture: In Search of the Shape of the Universe. New York: Walker Publishing Company, 2007.

Paur, Kathy. "The Fenchel-Nielsen Coordinates of Teichmuller Space." MIT Undergraduate Journal of Mathematics, vol. 1 (1999).

Peterson, Ivars. "Celestial Atomic Physics," Science News Online. week of Sept 10, 2005; vol 168, no 11. http://www.sciencenews.org/view/generic/id/6555/description/Celestial_Atomic_Physics (accessed 2007).

ll, Lisa. Warped Passages: Unraveling Mysteries of the Universe's Hidden Dimensions. New York: HarperPerennial. 2005.

Rockmore, Dan. Stalking the Riemann Hypothesis The Quest To Find the Hidden Law of Prime Numbers. New York: Vintage Books (division of Randomhouse), 2005.

Shackleton, Kenneth J. "Combinatorial Rigidity in Curve Complexes and Mapping Class Groups," Pacific Journal of Mathematics, vol. 230, no. 1 (March 2007).

Thurston, William P. "The Geometry and Topology of Three-Manifolds." Mathematical Sciences Research Institute. http://www.msri.org/publications/books/gt3m (accessed 2007).

Tobler, W.R. "Local Map Projections," The American Cartographer, vol. 1, no. 1 (1974).

Weeks, Jeffrey. "The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations," Notices of the AMS, vol. 51, no. 6 (June/July 2004).

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