MAA Reviews

Geometry: General

*** Banchoff, Thomas F. Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions New York, NY: Scientific American Library, 1990.

Blackwell, William. Geometry in Architecture New York, NY: John Wiley, 1984.

Bold, Benjamin. Famous Problems of Geometry and How to Solve Them Mineola, NY: Dover, 1982.

Burger, Dionys. Sphereland New York, NY: Thomas Y. Crowell, 1965.

** Croft, Hallard T.; Falconer, Kenneth J.; and Guy, Richard K. Unsolved Problems in Geometry New York, NY: Springer-Verlag, 1991.

* Fischer, Gerd, ed. Mathematical Models from the Collections of Universities and Museums, Wiesbaden: Friedr. Vieweg and Sohn, 1986. 2 Vols.

** Friedrichs, Kurt Otto. From Pythagoras to Einstein Washington, DC: Mathematical Association of America, 1965.

*** Hilbert, David and Cohn-Vossen, S. Geometry and the Imagination New York, NY: Chelsea, 1952.

*** Hildebrandt, Stefan and Tromba, Anthony J. Mathematics and Optimal Form New York, NY: Scientific American Library, 1984.

Ivins, William M., Jr. Art and Geometry: A Study in Space Intuitions Mineola, NY: Dover, 1964.

** Krause, Eugene F. Taxicab Geometry: An Adventure in Non-Euclidean Geometry Mineola, NY: Dover, 1986.

Lord, E.A. and Wilson, C.B. The Mathematical Description of Shape and Form New York, NY: Halsted Press, 1984.

March, Lionel and Steadman, Philip. The Geometry of Environment: An Introduction to Spatial Organization in Design Cambridge, MA: MIT Press, 1974.

Pottage, John. Geometrical Investigations: Illustrating the Art of Discovery in the Mathematical Field Reading, MA: Addison-Wesley, 1983.

* Row, T. Sundara. Geometric Exercises in Paper Folding Mineola, NY: Dover, 1966.

Rucker, Rudy. Geometry, Relativity, and the Fourth Dimension Mineola, NY: Dover, 1977.

* Stewart, Bonnie M. Adventures Among the Toroids, 4494 Wasau Road, Okemos, MI: 1970, 1980. Second Edition.

Geometry: Surveys

* Berger, Marcel, et al. Problems in Geometry New York, NY: Springer-Verlag, 1984.

* Berger, Marcel. Geometry, New York, NY: Springer-Verlag, 1987. 2 Vols.

* Cederberg, Judith N. A Course in Modern Geometries New York, NY: Springer-Verlag, 1989.

Court, Nathan A. College Geometry, New York, NY: Barnes and Noble, 1952. Second Edition.

Cox, Philip L. Geometry in Easy Steps: An Informal Approach Needham Heights, MA: Allyn and Bacon, 1983.

*** Coxeter, H.S.M. Introduction to Geometry, New York, NY: John Wiley, 1969. Second Edition.

*** Eves, Howard W. A Survey of Geometry, Boston, MA: Allyn and Bacon, 1972. Second Revised Edition.

Lial, Margaret L.; Steffensen, Arnold R.; and Johnson, L. Murphy. Essentials of Geometry for College Students Glenview, IL: Scott Foresman, 1990.

* Melzak, Z.A. Invitation to Geometry New York, NY: John Wiley, 1983.

* Millman, Richard S. and Parker, George D. Geometry: A Metric Approach with Models, New York, NY: Springer-Verlag, 1981, 1991. Second Edition.

* Pedoe, Dan. Geometry and the Visual Arts Mineola, NY: Dover, 1983. (Former title: Geometry and the Liberal Arts.)

Pedoe, Dan. Geometry: A Comprehensive Course Mineola, NY: Dover, 1988. (Former title: A Course of Geometry for Colleges and Universities.)

Postnikov, Mikhail. Lectures in Geometry, Moscow: MIR, 1982, 1986. 2 Vols.

Prenowitz, Walter and Jordan, M. Basic Concepts of Geometry New York, NY: John Wiley, 1965.

Smart, James R. Modern Geometries, Pacific Grove, CA: Brooks/Cole, 1973, 1988. Third Edition.

** Stehney, Ann K., et al., eds. Selected Papers on Geometry Washington, DC: Mathematical Association of America, 1979.

Tuller, Anita. A Modern Introduction to Geometries New York, NY: Van Nostrand Reinhold, 1967.

Geometry: School Geometry

* Bruni, James V. Experiencing Geometry Belmont, CA: Wadsworth, 1977.

Clemens, Stanley R.; O'Daffer, Phares G.; and Clooney, Thomas J. Geometry Reading, MA: Addison-Wesley, 1983.

* Fetisov, A.I. Proof in Geometry Moscow: MIR, 1978.

Hoffer, Alan. Geometry Reading, MA: Addison-Wesley, 1979.

** Jacobs, Harold R. Geometry, New York, NY: W.H. Freeman, 1974, 1986. Second Edition.

Kempe, A.B. How to Draw a Straight Line Reston, VA: National Council of Teachers of Mathematics, 1977.

* Konkle, Gail S. Shapes and Perceptions: An Intuitive Approach to Geometry Boston, MA: Prindle, Weber and Schmidt, 1974.

Loomis, E. The Pythagorean Proposition Reston, VA: National Council of Teachers of Mathematics, 1968.

* Moise, Edwin E. and Downs, Floyd L. Geometry Reading, MA: Addison-Wesley, 1975.

** O'Daffer, Phares G. and Clemens, Stanley R. Geometry: An Investigative Approach Reading, MA: Addison-Wesley, 1976.

Geometry: Euclidean and Non-Euclidean Geometry

Beskin, N.M. Dividing a Segment in a Given Ratio Moscow: MIR, 1975.

* Coxeter, H.S.M. Non-Euclidean Geometry Toronto: University of Toronto Press, 1957.

*** Coxeter, H.S.M., et al. Geometry Revisited Washington, DC: Mathematical Association of America, 1967.

* Dudley, Underwood. A Budget of Trisections New York, NY: Springer-Verlag, 1987.

* Faber, Richard L. Foundations of Euclidean and Non-Euclidean Geometry New York, NY: Marcel Dekker, 1983.

* Gans, David. An Introduction to Non-Euclidean Geometry New York, NY: Academic Press, 1973.

** Gray, Jeremy. Ideas of Space: Euclidean, Non-Euclidean, and Relativistic, New York, NY: Clarendon Press, 1979, 1989. Second Edition.

* Greenberg, Marvin Jay. Euclidean and Non-Euclidean Geometries: Development and History New York, NY: W.H. Freeman, 1974, 1980.

*** Hilbert, David. The Foundations of Geometry, La Salle, IL: Open Court, 1962, 1971. Tenth Edition.

Kelly, Paul J. and Matthews, Gordon. The Non-Euclidean, Hyperbolic Plane: Its Structure and Consistency New York, NY: Springer-Verlag, 1981.

Kogan, B. Yu. The Application of Mechanics to Geometry Chicago, IL: University of Chicago Press, 1974.

Lobachevski, N. The Theory of Parallels Peru, IL: Open Court, 1914.

* Martin, George E. The Foundations of Geometry and the Non-Euclidean Plane New York, NY: Springer-Verlag, 1975.

Moise, Edwin E. Elementary Geometry from an Advanced Standpoint, Reading, MA: Addison-Wesley, 1974. Second Edition.

Morley, F. and Morley, F.M. Inversive Geometry New York, NY: Chelsea, 1954.

Nikulin, V.V. and Shafarevich, Igor R. Geometries and Groups New York, NY: Springer-Verlag, 1987.

Pedoe, Dan. Circles: A Mathematical View Mineola, NY: Dover, 1979.

Posamentier, Alfred S. Excursions in Advanced Euclidean Geometry Reading, MA: Addison-Wesley, 1984.

Rosenfeld, B.A. and Sergeeva, N.D. Stereographic Projection Moscow: MIR, 1977.

Ryan, Patrick J. Euclidean and Non-Euclidean Geometry: An Analytical Approach New York, NY: Cambridge University Press, 1986.

Schwerdtfeger, Hans. Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry Mineola, NY: Dover, 1979.

Shreider, Yu. A. What is Distance? Chicago, IL: University of Chicago Press, 1974.

* Szmielew, Wanda. From Affine to Euclidean Geometry: An Axiomatic Approach Norwell, MA: D. Reidel, 1983.

Trudeau, Richard J. The Non-Euclidean Revolution New York, NY: Birkhauser, 1987.

Vaisman, Izu. Foundations of Three-Dimensional Euclidean Geometry New York, NY: Marcel Dekker, 1980.

Yaglom, I.M. A Simple Non-Euclidean Geometry and Its Physical Basis New York, NY: Springer-Verlag, 1979.

* Yates, Robert C. The Trisection Problem Reston, VA: National Council of Teachers of Mathematics, 1971.

Geometry: Polyhedra, Tilings, Symmetry

** Armstrong, M.A. Groups and Symmetry New York, NY: Springer-Verlag, 1988.

* Baglivo, Jenny A. and Graver, Jack E. Incidence and Symmetry in Design and Architecture New York, NY: Cambridge University Press, 1983.

Beskin, N.M. Images of Geometric Solids Moscow: MIR, 1985.

* Bunch, Bryan H. Reality's Mirrors: Exploring the Mathematics of Symmetry New York, NY: John Wiley, 1989.

Coxeter, H.S.M. Regular Polytopes, Mineola, NY: Dover, 1973. Third Edition.

* Coxeter, H.S.M., et al., eds. M.C. Escher: Art and Science New York, NY: Elsevier Science, 1986.

** Cundy, M.H. and Rollett, A.P. Mathematical Models New York, NY: Clarendon Press, 1961.

*** Grunbaum, Branko and Shephard, G.C. Tilings and Patterns New York, NY: W.H. Freeman, 1986, 1989.

* Grunbaum, Branko. Convex Polytopes New York, NY: John Wiley, 1967.

Hargittai, Istvan, ed. Symmetry: Unifying Human Understanding Elmsford, NY: Pergamon Press, 1986.

* Henderson, Linda D. The Fourth Dimension and Non-Euclidean Geometry in Modern Art Princeton, NJ: Princeton University Press, 1983.

* Hilton, Peter J. and Pedersen, Jean. Build Your Own Polyhedra Reading, MA: Addison-Wesley, 1988.

* Holden, Alan. Shapes, Space, and Symmetry New York, NY: Columbia University Press, 1971.

Holden, Alan. Orderly Tangles: Cloverleafs, Gordian Knots, and Regular Polylinks New York, NY: Columbia University Press, 1983.

Kavanau, J. Lee. Symmetry: An Analytical Treatment West Los Angeles, CA: Science Software Systems, 1980.

* Lockwood, E.H. and Macmillan, R.H. Geometric Symmetry New York, NY: Cambridge University Press, 1978.

Loeb, Arthur L. Space Structures: Their Harmony and Counterpoint Reading, MA: Addison-Wesley, 1976.

Loeb, Arthur L. Color and Symmetry New York, NY: John Wiley, 1971.

Lyndon, Roger C. Groups and Geometry New York, NY: Cambridge University Press, 1985.

MacGillavry, Caroline H. Fantasy Symmetry: The Periodic Drawings of M.S. Escher New York, NY: Harry N. Abrams, 1976.

* Martin, George E. Transformation Geometry: An Introduction to Symmetry New York, NY: Springer-Verlag, 1982.

Pearce, Peter and Pearce, Susan. Polyhedra Primer New York, NY: Van Nostrand Reinhold, 1978.

Pugh, Anthony. Polyhedra: A Visual Approach Berkeley, CA: University of California Press, 1976.

Ranucci, E.R. and Teeters, J.L. Creating Escher-Type Drawings Palo Alto, CA: Creative Publ., 1977.

* Rosen, Joe. Symmetry Discovered: Concepts and Applications in Nature and Science New York, NY: Cambridge University Press, 1975.

** Schattschneider, Doris J. Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M.C. Escher New York, NY: W.H. Freeman, 1990.

* Senechal, Marjorie and Fleck, George, eds. Patterns of Symmetry Amherst, MA: University of Massachusetts Press, 1977.

** Senechal, Marjorie and Fleck, George, eds. Shaping Space: A Polyhedral Approach New York, NY: Birkhauser, 1988.

Shubnikov, A.V. and Koptsik, V.A. Symmetry in Science and Art New York, NY: Plenum Press, 1974.

Stevens, Peter S. Patterns in Nature Waltham, MA: Little, Brown, 1974.

* Toth, L. Fejes. Regular Figures Elmsford, NY: Pergamon Press, 1964.

Wenninger, Magnus J. Spherical Models New York, NY: Cambridge University Press, 1979.

* Wenninger, Magnus J. Polyhedron Models New York, NY: Cambridge University Press, 1971.

*** Weyl, Hermann. Symmetry Princeton, NJ: Princeton University Press, 1952.

Geometry: Geometric Transformations

* Bakel'man, I. Ya. Inversions Chicago, IL: University of Chicago Press, 1974.

Eccles, Frank M. An Introduction to Transformational Geometry Reading, MA: Addison-Wesley, 1971.

* Gans, David. Transformations and Geometries Englewood Cliffs, NJ: Appleton-Century-Crofts, 1969.

** Yaglom, I.M. Geometric Transformations, Washington, DC: Mathematical Association of America, 1962--73. 3 Vols.

Geometry: Projective Geometry

* Blumenthal, Leonard M. Modern View of Geometry Mineola, NY: Dover, 1980.

** Coxeter, H.S.M. Projective Geometry, Toronto: University of Toronto Press, 1974. Second Edition.

* Coxeter, H.S.M. The Real Projective Plane New York, NY: Cambridge University Press, 1961.

Dorwart, Harold L. Geometry of Incidence Englewood Cliffs, NJ: Prentice Hall, 1966.

Fishback, William T. Projective and Euclidean Geometry, New York, NY: John Wiley, 1969. Second Edition.

Garner, Lynn E. An Outline of Projective Geometry Amsterdam: North-Holland, 1981.

Hirschfeld, J.W.P. Projective Geometries Over Finite Fields New York, NY: Clarendon Press, 1979.

Hirschfeld, J.W.P. Finite Projective Spaces of Three Dimensions New York, NY: Clarendon Press, 1985.

Penna, Michael A. and Patterson, Richard R. Projective Geometry and Its Applications to Computer Graphics Englewood Cliffs, NJ: Prentice Hall, 1986.

Samuel, Pierre. Projective Geometry New York, NY: Springer-Verlag, 1988.

* Veblen, Oswald and Young, John Wesley. Projective Geometry, New York, NY: Blaisdell, 1938, 1946. 2 Vols.

Wylie, Clarence R. Introduction to Projective Geometry New York, NY: McGraw-Hill, 1970.

* Young, John Wesley. Projective Geometry Washington, DC: Mathematical Association of America, 1930.

Geometry: Computational Geometry

** Abelson, Harold and diSessa, Andrea A. Turtle Geometry: The Computer as a Medium for Exploring Mathematics Cambridge, MA: MIT Press, 1981.

Billstein, Rick; Libeskind, S.; and Lott, Johnny W. Logo Redwood City, CA: Benjamin Cummings, 1985.

Clayson, J. Visual Modeling with Logo Cambridge, MA: MIT Press, 1988.

Edelsbrunner, H. Algorithms in Computational Geometry New York, NY: Springer-Verlag, 1987.

** O'Rourke, Joseph. Art Gallery Theorems and Algorithms New York, NY: Oxford University Press, 1987.

* Preparata, Franco P. and Shamos, Michael I. Computational Geometry: An Introduction New York, NY: Springer-Verlag, 1985.

Toussaint, G., ed. Computational Geometry Amsterdam: North-Holland, 1985.

Geometry: Discrete and Combinatorial Geometry

Ambartzumian, R.V. Combinatorial Integral Geometry with Applications to Mathematical Stereology New York, NY: John Wiley, 1982.

Batten, Lynn Margaret. Combinatorics of Finite Geometries New York, NY: Cambridge University Press, 1986.

* Boltyanskii, Vladimir G. Equivalent and Equidecomposable Figures Lexington, MA: D.C. Heath, 1963.

** Boltyanskii, Vladimir G. Hilbert's Third Problem Silver Spring, MD: V.H. Winston, 1978.

* Boltyanskii, Vladimir G. and Gohberg, Israel. The Decomposition of Figures into Smaller Parts Chicago, IL: University of Chicago Press, 1980.

* Boltyanskii, Vladimir G. and Gohberg, Israel. Results and Problems in Combinatorial Geometry New York, NY: Cambridge University Press, 1985.

** Bonnesen, T. and Fenchel, W. Theory of Convex Bodies Moscow, ID: BCS Associates, 1987.

* Hadwiger, Hugo and Debrunner, Hans. Combinatorial Geometry in the Plane New York, NY: Holt, Rinehart and Winston, 1964.

** Kazarinoff, Nicholas D. Geometric Inequalities Washington, DC: Mathematical Association of America, 1961, 1975.

Kelly, Paul J. and Weiss, Max L. Geometry and Convexity: A Study in Mathematical Methods New York, NY: John Wiley, 1979.

** Lay, Steven R. Convex Sets and Their Applications New York, NY: John Wiley, 1982.

* Ledermann, Walter and Vajda, Steven, eds. Geometry and Combinatorics New York, NY: John Wiley, 1985. Handbook of Applicable Mathematics, Volume V.

** Mitrinovic, Dragoslav S.; Pe caric, J.E.; and Volenec, V. Recent Advances in Geometric Inequalities Norwell, MA: Kluwer Academic, 1989.

Moser, William. Problems in Discrete Geometry, Toronto: McGill-Queen's University Press, 1979, 1980. Fifth Edition.

Prenowitz, Walter and Jantosciak, James. Join Geometries: A Theory of Convex Sets and Linear Geometry New York, NY: Springer-Verlag, 1979.

* Yaglom, I.M. and Boltyanskii, Vladimir G. Convex Figures New York, NY: Holt, Rinehart and Winston, 1961.

Geometry: Differential Geometry

Abraham, Ralph H.; Marsden, Jerrold E.; and Ratiu, T. Manifolds, Tensor Analysis, and Applications New York, NY: Springer-Verlag, 1988.

* Arnold, V.I. Catastrophe Theory, New York, NY: Springer-Verlag, 1984, 1986. Second Edition.

Berger, Marcel and Gostiaux, Bernard. Differential Geometry: Manifolds, Curves, and Surfaces New York, NY: Springer-Verlag, 1988.

* Boothby, William M. An Introduction to Differentiable Manifolds and Riemannian Geometry, New York, NY: Academic Press, 1975, 1986. Second Edition.

* Burke, William L. Applied Differential Geometry New York, NY: Cambridge University Press, 1985.

* Dodson, C.T.J. and Poston, Tim. Tensor Geometry: The Geometric Viewpoint and its Uses Brooklyn, NY: Pitman, 1977.

Faber, Richard L. Differential Geometry and Relativity Theory: An Introduction New York, NY: Marcel Dekker, 1983.

Flanders, Harley. Differential Forms with Applications to the Physical Sciences Mineola, NY: Dover, 1989.

Hopf, Heinz. Differential Geometry in the Large New York, NY: Springer-Verlag, 1983.

** Hsiung, Chuan-Chih. A First Course in Differential Geometry New York, NY: John Wiley, 1981.

Kahn, Donald W. Introduction to Global Analysis New York, NY: Academic Press, 1980.

* Kobayashi, Shoshichi and Nomizu, Katsumi. Foundations of Differential Geometry, New York, NY: John Wiley, 1963--69. 2 Vols.

Lu, Yung-Chen. Singularity Theory and an Introduction to Catastrophe Theory New York, NY: Springer-Verlag, 1976.

Marmo, Giuseppe, et al. Dynamical Systems: A Differential Geometric Approach to Symmetry and Reduction New York, NY: John Wiley, 1985.

* Millman, Richard S. and Parker, George D. Elements of Differential Geometry Englewood Cliffs, NJ: Prentice Hall, 1977.

O'Neill, Barrett. Elementary Differential Geometry New York, NY: Academic Press, 1966.

** Spivak, Michael D. A Comprehensive Introduction to Differential Geometry, Boston, MA: Publish or Perish, 1970--79. Second Edition,

Stoker, J.J. Differential Geometry New York, NY: John Wiley, 1969.

** Struik, Dirk Jan. Lectures on Classical Differential Geometry, Mineola, NY: Dover, 1988. (Former title: Differential Geometry.)

Thorpe, John A. Elementary Topics in Differential Geometry New York, NY: Springer-Verlag, 1979.

Veblen, Oswald and Whitehead, J.H.C. The Foundations of Differential Geometry New York, NY: Cambridge University Press, 1967.

** do Carmo, Manfredo P. Differential Geometry of Curves and Surfaces Englewood Cliffs, NJ: Prentice Hall, 1976.

Geometry: Algebraic Geometry

* Brieskorn, Egbert and Knorrer, Horst. Plane Algebraic Curves New York, NY: Birkhauser, 1986.

Bruce, J.W. and Giblin, P.J. Curves and Singularities: A Geometrical Introduction to Singularity Theory New York, NY: Cambridge University Press, 1984.

Clemens, C. Herbert. A Scrapbook of Complex Curve Theory New York, NY: Plenum Press, 1980.

Fulton, William. Algebraic Curves: An Introduction to Algebraic Geometry Reading, MA: W.A. Benjamin, 1969.

Griffiths, Phillip A. Introduction to Algebraic Curves Providence, RI: American Mathematical Society, 1989.

Griffiths, Phillip A. and Harris, Joseph. Principles of Algebraic Geometry New York, NY: John Wiley, 1978.

* Kendig, Keith. Elementary Algebraic Geometry New York, NY: Springer-Verlag, 1987.

Orzech, Grace and Orzech, Morris. Plane Algebraic Curves: An Introduction Via Valuations New York, NY: Marcel Dekker, 1981.

* Reid, Miles. Undergraduate Algebraic Geometry New York, NY: Cambridge University Press, 1988.

* Seidenberg, A. Elements of the Theory of Algebraic Curves Reading, MA: Addison-Wesley, 1968.

Seidenberg, A., ed. Studies in Algebraic Geometry Washington, DC: Mathematical Association of America, 1980.

Semple, J.G. and Kneebone, G.T. Algebraic Curves New York, NY: Oxford University Press, 1959.

* Semple, J.G. and Roth, L., eds. Introduction to Algebraic Geometry New York, NY: Oxford University Press, 1985.

** Shafarevich, Igor R. Basic Algebraic Geometry New York, NY: Springer-Verlag, 1974.

Walker, Robert J. Algebraic Curves New York, NY: Springer-Verlag, 1978.

Geometry: Special Topics

Artzy, Rafael. Linear Geometry Reading, MA: Addison-Wesley, 1974.

* Dembowski, P. Finite Geometries New York, NY: Springer-Verlag, 1968.

Edmondson, Amy C. A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller New York, NY: Birkhauser, 1987.

Gordon, V.O. and Sementsov-Ogievskii, M.A. A Course in Descriptive Geometry Moscow: MIR, 1980.

Hammer, J. Unsolved Problems Concerning Lattice Points Brooklyn, NY: Pitman, 1977.

Hughes, D.R. and Piper, F.C. Design Theory, New York, NY: Cambridge University Press, 1985, 1988. Second Edition.

** Lockwood, E.H. A Book of Curves New York, NY: Cambridge University Press, 1960.

Lyusternik, L.A. The Shortest Lines: Variational Problems Moscow: MIR, 1976, 1983.

* Mortenson, Michael E. Geometric Modeling New York, NY: John Wiley, 1985.

Porteous, Ian R. Topological Geometry, New York, NY: Cambridge University Press, 1981. Second Edition.

Pugh, Anthony. An Introduction to Tensegrity Berkeley, CA: University of California Press, 1976.

Santalo, Luis A. Integral Geometry and Geometric Probability Reading, MA: Addison-Wesley, 1976.

Schuster, Seymour. Elementary Vector Geometry New York, NY: John Wiley, 1962.

* Snapper, Ernst and Troyer, Robert J. Metric Affine Geometry Mineola, NY: Dover, 1989.

* Yates, Robert C. Curves and Their Properties Reston, VA: National Council of Teachers of Mathematics, 1974.