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.