Useful Texts for MATH 5210/7210
Transformations
The following books contain discussions of transformation geometry with viewpoints similar to our course:
Discovering Geometry, An Investigative Approach, third edition, by Michael Serra, Key Curriculum Press. This innovative high school textbook emphasizes visualization, experimentation, writing, and cooperative problem solving. Chapter 7, Transformations and Tessellations, is a nice example of how to present transformations to high school students.
Schaum's Outline of Geometry, third edition, by Barnett Rich, revised by Philip Schmidt, McGraw-Hill 2000. Chapter 17: Transformational Geometry.
Geometry Revisited, by H. S. M. Coxeter and S. L. Greitzer, Mathematical Association of America 1967. Chapter 4: Transformations.
Geometric Transformations I, by I. M. Yaglom, Mathematical Association of America 1962. This book has lots of challenging problems, and their solutions take up half the book!
Schaum's Outline of Beginning Linear Algebra, by Seymour Lipschutz, McGraw-Hill 1996. This is a good review of the linear algebra you need to understand Euclidean transformations. Especially useful are Chapter 8, Linear Mappings, and Chapter 9, Linear Mappings and Matrix Representations.
Symmetry
Symmetry, by Hans Walser, Mathematical Association of America 2000.
Groups and Symmetry, A Guide to Discovering Mathematics, by David Farmer, American Mathematical Society 1996. Chapter 2: The Rigid Motions of the Plane.
"The plane symmetry groups: their recognition and notation," by Doris Schattschneider, American Math. Monthly, vol. 85, no. 6, June-July 1978. This is a great general introduction to the math of wallpaper patterns.
Tilings and Patterns, by Branko Grunbaum and G. C. Shephard, W. H. Freeman, New York 1987 (Introduction and Chapter 1). This is a very complete reference on plane symmetry. A lot of it is quite technical, but it also has excellent illustrations and lots of references.
Polyhedra
Books in print
All are available from amazon.com.
Bucky Works: Buckminster Fuller's Ideas for Today, by J. Baldwin, Wiley 1997. (applications to architecture)
Order in Space, by Keith Critchlow, Thames and Hudson 2000. (applications to architecture)
Polyhedra, by Peter Cromwell, Cambridge 1997.
Mathematical Models, by H.M. Cundy and A.P. Rollett, Tarquin 1997.
The Nature of Solids, by Alan Holden, Dover. (applications to chemistry)
Shapes, Space, and Symmetry, by Alan Holden, Dover.
Timaeus, by Plato, translated by Donald Zeyl, Hackett 2000. (history)
On Growth and Form, by Sir D'Arcy Thompson, Dover. (applications to biology)
Polyhedron Models, by Magnus J. Wenninger, Cambridge 1974.
Books out of print
All are available in libraries; some used copies can be ordered from amazon.com.
Domebook 2, third edition, by L. Kahn (ed.), Random House 1974. (applications to architecture)
The Architecture of Molecules, by L. Pauling and R. Hayward, Freeman 1964. (applications to chemistry)
The Dome Builder's Handbook, by J. Prenis, Running Press 1973. (applications to architecture)
Polyhedra, A Visual Approach, by A. Pugh, University of California 1976.
Shaping Space: A Polyhedral Approach, by Marjorie Senechal and George Fleck (eds.), Birkhauser 1988. This book is in the UGA main library (N7430.5.S52 1988). It has a very large list of references and lots of chapters on teaching.
The Third Dimension in Chemistry, by A.F. Wells, Oxford 1956. (applications to chemistry)
Three-Dimensional Nets and Polyhedra, by A.F. Wells, Wiley 1977. (applications to chemistry)