Geometry

1. Liang-shin Hahn, Complex Numbers and Geometry
   • Spectrum Series.
   • Mathematical Association of America 1994.

2. David Hilbert, Foundations of Geometry
   • Second English Edition
   • Open Court Publishing Company
   • LaSalle, Illinois, 1971
   • Seventh printing 1994
   • Chapter IV: Theory of Plane Area (Equidecomposability, etc.)

3. Robin Hartshorne, Companion to Euclid
   • A course of geometry, based on Euclid's Elements from a modern point of view.
   • Berkeley Mathematics Lecture Notes, Volume 9.
   • American Mathematical Society 1997.
   • Equidecomposition of simple plane polygons and the Bolyai-Gerwien Theorem are discussed in Chapter 5; and the non-Euclidean version on page 259.
   • How to order from: AMS Book Store and information on current edition.
     Last changed: April 1, 1999.

4. Vladimir Grigorevich Boltyanskii, Equivalent and Equidecomposable Figures
   • Translated and adapted from the 1st Russian ed. (1956) by Alfred K. Henn and Charles E. Watts.
   • Boston, Heath 1963
   • The Bolyai-Gerwien Theorem and its impossibility in dimension three.

5. Subrahmanyan Chandrasekhar, NEWTON'S PRINCIPIA for the Common Reader
   • Oxford University Press 1995.

6. William P. Thurston, Three-Dimensional Geometry and Topology
   • Edited by Silvio Levy
   • Princeton University Press, 1997
   • Princeton mathematical series, No. 35
   • Hyperbolic Geometry & Topology of Three-manifolds.
   • The Web-Site: Geometry and the Imagination in Minneapolis
     

7. Colin C. Adams, The KNOT BOOK
   • An Elementary Introduction to the Mathematical Theory of Knots.
   • W. H. Freeman and Company, New York, 1994.

8. W.B. Raymond Lickorish, An Introduction to Knot Theory
   • Graduate Texts in Mathematics 175.
   • Springer-Verlag, New York, 1997.

9. Alain Connes, Noncommutative Geometry
   • Measure Theory, K-Theory, Differential Geometry, Quantized Calculus, Operator Algebras, Yang-Mills Action, Symmetry Breaking, The Glashow-Weiberg-Salam Standard Model.
   • Academic Press, Inc., New York, 1994. (Not for the timid!)

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