Symbols (continued)

Symbols (continued)

Other

dim(S)

The dimension of set S

Is in perspective with respect to

H(AB, CD)

Point D is the harmonic conjugate of C with respect to A and B

The hyperplane at infinity

Relations

Equals

Is not equal to

Is approximately equal to

Equals (used for ratios)

Is directly proportional to

Is congruent to

Is not congruent to

Is isomorphic to

Is not isomorphic to

Numbers

e The Euler number, the base of the natural logarithms

Is equivalent to; if and only if

Not

Not; used over any other symbol to negate its meaning

There exists

For all

Therefore

Since; because

Such that

j or h

End of proof

CHARTS & TABLES

Symbols Beginning – Ending

Recommended Reading APPENDIX

Recommended Reading

Introductory Level

Abbott, Edwin Abbott. Flatland. Princeton, N.J.: Princeton University Press, 1991. Banchoff, Thomas F. Beyond the Third Dimension: Geometry, Computer

Graphics, and Higher Dimensions. New York: Scientific American Library, 1996.

Cederberg, Judith N. A Course in Modern Geometries. New York: Springer- Verlag, 2000. Coxeter, H. S. M., and S. L. Greitzer. Geometry Revisited. New York: L. W. Singer, 1967. Cromwell, Peter R. Polyhedra. Cambridge, U.K.: Cambridge University Press, 1999. Crowe, Donald W., and Dorothy K. Washburn. Symmetries of Culture: Theory and Practice of Plane Pattern Analysis. Seattle: University of Washington Press, 1988.

Davis, Philip J. Spirals: From Theodorus to Chaos. Wellesley, MA: A K Peters, 1993. Densmore, Dana, ed. Thomas L. Heath, trans. Euclid’s Elements. Santa Fe, N.Mex.: Green Lion Press, 2002. Devaney, Robert L. Chaos, Fractals and Dynamics: Computer Experiments in Mathematics. Reading, Mass.: Addison-Wesley, 1990. Edmondson, Amy C. A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller. Boston: Birkhäuser, 1987. El-Said, Issam, and Ayse Parmen. Geometric Concepts in Islamic Art. Palo Alto, Calif.: Dale Seymour Publications, 1976. Francis, Richard L. The Mathematician’s Coloring Book. Lexington, Mass.: COMAP, 1989. Friedrichs, K. O. From Pythagoras to Einstein. Washington, D.C.: MAA, 1965. Gay, David. Geometry by Discovery. New York: John Wiley, 1998. Gerdes, Paulus. Geometry from Africa: Mathematical and Educational

Explorations. Washington, D.C.: MAA, 1999. Hansen, Vagn Lundsgaard. Geometry in Nature. Wellesley, Mass.: A K Peters, 1994. Hargittai, István, and Magdolna Hargittai. Symmetry: A Unifying Concept. Bolinas, Calif.: Shelter Publications, 1994. Heath, Thomas L., ed. The Thirteen Books of Euclid’s Elements. New York: Dover Publications, 1956. Heilbron, J. L. Geometry Civilized: History, Culture, and Technique. Oxford, U.K.: Oxford University Press, 2000.

Recommended Reading APPENDIX

APPENDIX

Recommended Reading

van Hiele, Pierre M. Structure and Insight. San Diego, Calif.: Academic Press,

1997. Henderson, David W. Experiencing Geometry in Euclidean, Spherical, and Hyperbolic Spaces. Upper Saddle River, N.J.: Prentice Hall, 2001. Honsberger, Ross. Episodes in Nineteenth and Twentieth Century Euclidean

Geometry. Washington, D.C.: MAA, 1995. Kappraff, Jay. Connections: The Geometric Bridge between Art and Science.

New York: McGraw-Hill, 1991. King, James. Geometry through Circles with the Geometer’s Sketchpad.

Emeryville, Calif.: Key Curriculum Press, 1996. King, James, and Doris Schattschneider, eds. Geometry Turned On: Dynamic Software in Learning, Teaching, and Research. Washington, D.C.: MAA, 1997.

Krause, Eugene F. Taxicab Geometry: An Adventure in Non-Euclidean

Geometry. New York: Dover Publications, 1986. Lénárt, István. Non-Euclidean Adventures on the Lénárt Sphere. Emeryville,

Calif.: Key Curriculum Press, 1996. Martin, George E. Transformation Geometry. New York: Springer-Verlag, 1982. McLeay, Heather. The Knots Puzzle Book. Emeryville, Calif.: Key Curriculum

Press, 2000. Meyer, Walter. Geometry and Its Applications. San Diego, Calif.: Academic

Press, 1999. Muller, Jim. The Great Logo Adventure. Austin, Tex.: Doone Publications, 1997. Olds, C. D., Anneli Lax, and Giuliana Davidoff. The Geometry of Numbers.

Washington, D.C.: MAA, 2000. Pedoe, Dan. Circles: A Mathematical View. Washington, D.C.: MAA, 1995. ———. Geometry and the Visual Arts. New York: Dover Publications, 1983. Posamentier, Alfred. Advanced Euclidean Geometry: Excursions for Students

and Teachers. Emeryville, Calif.: Key Curriculum Press, 2002. Posamentier, Alfred, and William Wernick. Advanced Geometric Constructions.

Palo Alto, Calif.: Dale Seymour Publications, 1988. Ranucci, E. R., and J. E. Teeters. Creating Escher-Type Drawings. Palo Alto,

Calif.: Creative Publications, 1977. Schattschneider, Doris. Visions of Symmetry: Notebooks, Periodic Drawings, and Related Works of M. C. Escher. New York: W. H. Freeman, 1990. Senechal, Marjorie, and George Fleck. Shaping Space. Boston: Birkhäuser, 1988. Serra, Michael. Discovering Geometry: An Inductive Approach. Emeryville,

Calif.: Key Curriculum Press, 1997. Smart, James R. Modern Geometries. Pacific Grove, Calif.: Brooks/Cole, 1998. Thompson, D’Arcy W. On Growth and Form. New York: Dover Publications,

1992. Trudeau, Richard J. The Non-Euclidean Revolution. Boston: Birkhäuser, 1987.

APPENDIX

Recommended Reading

Recommended Reading APPENDIX

de Villiers, Michael. Rethinking Proof with The Geometer’s Sketchpad. Emeryville, Calif.: Key Curriculum Press, 1999. Weeks, Jeffrey. Exploring the Shape of Space. Emeryville, Calif.: Key Curriculum Press, 2001.

Videos, Software, and Websites

Amenta, Nina. Kali. Software for Macintosh and Windows. Available online. URL:http://humber.northnet.org/weeks/. Clarke, Arthur C. Fractals: The Colors of Infinity. Princeton, N.J.: Films for the Humanities and Sciences, 1997. VHS. 30 minutes. Devaney, Robert L. Professor Devaney Explains the Fractal Geometry of the Mandelbrot Set. Emeryville, Calif.: Key College Publishing. VHS. 70 minutes. ———. “The Geometry Junkyard.” Available online. URL: http://www1.ics.uci.edu/~eppstein/junkyard/. The Geometry Center. Not Knot. Wellesley, Mass.: A K Peters, 1991. VHS. 16 minutes. ———. Outside In. Wellesley, Mass.: A K Peters, 1994. VHS. 22 minutes. ———. KaleidoTile. Minneapolis: The Geometry Center. Software for

Macintosh. Available online. URL: http://humber.northnet.org/weeks/. Jackiw, Nick. The Geometer’s Sketchpad Dynamic Geometry Software. Emeryville, Calif.: Key Curriculum Press, 2001. Software for Macintosh and Windows.

Laborde, Jean-Marie, and F. Bellemain. Cabri Geometry II. Dallas, Tex.: Texas Instruments, 1994. Software for Macintosh and Windows. Lee, Kevin. KaleidoMania! Emeryville, Calif.: Key Curriculum Press, 2000. Software for Macintosh and Windows. Weeks, Jeffrey. The Shape of Space. Emeryville, Calif.: Key College Publishing, 2000. VHS. 20 minutes. Weisstein, Eric. World of Mathematics. Available online. URL: http://mathworld.wolfram.com/.

Classroom Resources

Frame, Michael, and Benoit B. Mandelbrot. Fractals, Graphics, and Mathematics Education. Washington, D.C.: MAA, 2002. Lindquist, Mary Montgomery, and Albert P. Shulte, eds. Learning and Teaching Geometry, K-12. Reston, Va.: NCTM, 1987. Mammana, Carnelo, and Vinicio Villani, eds. Perspectives on the Teaching of Geometry for the 21st Century: ICMI Study. Dordrecht, Netherlands: Kluwer, 1998.

Recommended Reading APPENDIX

APPENDIX

Recommended Reading

National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. Reston, Va.: NCTM, 2000. ———. Navigating through Geometry in Grades 3–5. Reston, Va.: NCTM, 2001. ———. Navigating through Geometry in Grades 6–8. Reston, Va.: NCTM, 2001. ———. Navigating through Geometry in Grades 9–12. Reston, Va.: NCTM,

2001. ———. Navigating through Geometry in Prekindergarten–Grade 2. Reston,

Va.: NCTM, 2001.