Adventures in the MathZone: Online Biliography

A list of Web articles, books, and other resources on various mathematical topics.

The Jungles of Randomness

Mathematics and Art

General References

Peterson, I. 2002. Mathematical Treks: From Surreal Numbers to Magic Circles. Washington, D.C.: Mathematical Association of America.

______. 1998. The Mathematical Tourist: New and Updated Snapshots of Modern Mathematics. New York: W.H. Freeman.

Peterson, I., and N. Henderson. Math Trek: Adventures in the MathZone. New York: Wiley.

______. Math Trek 2: A Mathematical Space Odyssey. New York: Wiley.

MythMath

Snow

Adler, J., and N. Price. 1991. The melting of a mighty myth. Newsweek (July 22):63.

Brody, J.E. 1988. For snow, the real action begins after it falls. New York Times (Feb. 9).

Derby, S.P. 1994. Eskimo words for snow derby. Available at http://tafkac.org/language/eskimo_words_for_snow_derby.html.

Devlin, K. 1997. Eskimo pi. MAA Online (February). Available at http://www.maa.org/devlin/devlin_2_97.html.

Hoeg, P. 1993. Smilla's Sense of Snow. New York: Farrar, Straus and Giroux.

Pullum, G.K. 1991. The Great Eskimo Vocabulary Hoax. Chicago: University of Chicago Press.

Woodbury, A.C. 1991. Counting Eskimo words for snow: A citizen's guide. Available at http://www.princeton.edu/~browning/snow.html.

Lemmings

Chitty, D. 1996. Do Lemmings Commit Suicide? Beautiful Hypotheses and Ugly Facts. New York: Oxford University Press.

Kruszelnicki, K.S. 2004. Lemmings suicide myth. Australian Broadcasting Corporation Online. Available at http://www.abc.net.au/science/k2/moments/s1081903.htm.

Woodford, R. 2003. Lemming suicide myth: Disney film faked bogus behavior. Alaska Wildlife News (September). Article.

White Wilderness
http://www.snopes.com/disney/films/lemmings.htm
Urban Legends Reference Pages

Bumblebee Flight

Brookes, M. 1997. On a wing and a vortex. New Scientist (Oct. 11):24-27.

Cormier, R. 1991. The Bumblebee Flies Anyway. New York: Random House.

Dalton, S. 1975. Borne on the Wind: The Extraordinary World of Insects in Flight. New York: Reader's Digest Press.

Dickinson, M. 2001. Solving the mystery of insect flight. Scientific American 284(June):34-41. Article.

Dudley, R. 1999. The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton, N.J.: Princeton University Press.

Macphee, K. 2002. The buzz on bumblebees. Plus (Jan. 11). Available at http://www.pass.maths.org.uk/issue17/news/bumble/index.html.

McMasters, J.H. 1989. The flight of the bumblebee and related myths of entomological engineering. American Scientist 77(March-April):164-169.

Pennicott, K. 2001. Lasers illuminate the flight of the bumblebee. PhysicsWeb (Oct. 16). Available at http://www.physicsweb.org/article/news/5/10/9.

Peterson, I. 2004. Flight of the bumblebee. Science News Online (Sept. 11). Available at http://www.sciencenews.org/articles/20040911/mathtrek.asp.

Segelken, R. 2000. Insect flight obeys the principles of aerodynamics, CU physicist proves. Cornell Chronicle 31(March 30). Available at http://www.news.cornell.edu/Chronicle/00/3.30.00/insect_flight.html.

Siskind, B. 2004. Bumblebees Can't Fly: Seven Simple Strategies for Making the Impossible Possible. New York: Wiley.

Wang, Z.J. 2000. Two dimensional mechanism for insect hovering. Physical Review Letters 85(Sept. 4):2216-2219. Abstract available at http://link.aps.org/abstract/PRL/v85/p2216.

Wootton, R.J. 1990. The mechanical design of insect wings. Scientific American 263(November):114-120.

Zetie, K. 2003. Getting a buzz from flight. Physics Education 38(November):476. Available at http://www.iop.org/EJ/article/0031-9120/38/6/M02/pe3_6_m02.pdf.

______. 1996. The strange case of the bumble-bee that flew. Physics World (October):72. Available at http://www.wolfson.ox.ac.uk/~ben/zetie1.htm.

Pi

Bailey, D.H., J.M. Borwein, P.B. Borwein, and S. Plouffe. 1997. The quest for pi. Mathematical Intelligencer 19(No. 1):50-57. Available at http://www.cecm.sfu.ca/personal/pborwein/PISTUFF/Apistuff.html.

Beckmann, P. 1971. A History of Pi. New York: St. Martin's Press.

Blatner, D. 1997. The Joy of Pi. New York: Walker. See http://www.joyofpi.com/.

Dudley, U. 1992. Legislating pi. In Mathematical Cranks. Washington, D.C.: Mathematical Association of America.

Gardner, M. 1999. Slicing pi into millions. In Gardner's Whys & Wherefores. Amherst, N.Y.: Prometheus Books.

Keith, M. Preprint. The pi code. Available at http://users.aol.com/s6sj7gt/picode.htm.

______. Preprint. Lady pi. Available at http://users.aol.com/s6sj7gt/ladypi.htm.

Peterson, I. 2002. A trillion pieces of pi. Science News Online (Dec. 14). Available at http://www.sciencenews.org/articles/20021214/mathtrek.asp.

______. 2001. Pi à la mode. Science News 160(Sept. 1):136-137. Available at http://www.sciencenews.org/20010901/bob9.asp.

______. 2000. The incredible pi code. Science News Online (April 1). Available at http://www.sciencenews.org/articles/20000401/mathtrek.asp.

______. 2000. Sliding pi. Science News Online (June 3). Available at http://www.sciencenews.org/articles/20000603/mathtrek.asp.

______. 1999. A song about pi. Science News Online (July 10). Available at http://www.sciencenews.org/pages/sn_arc99/7_10_99/mathland.htm.

______. 1998. Pick a digit, any digit. Science News Online (Feb. 28). Available at http://www.sciencenews.org/pages/sn_arc98/2_28_98/mathland.htm.

______. 1997. A passion for pi. Science News Online (Aug. 8). Available at http://www.sciencenews.org/pages/sn_arc97/8_2_97/mathland.htm.

Singmaster, D. 1985. The legal values of pi. Mathematical Intelligencer 7(No. 2):69-72.

Watson, B. 2000. Squaring the circle is no piece of pi. Smithsonian 31(May):71-82. Summary available at http://www.smithsonianmag.si.edu/smithsonian/issues00/may00/pi.html.

For additional information about pi, check the Pi Pages at http://www.cecm.sfu.ca/personal/jborwein/pi_cover.html.

Indiana bill sets the value of pi to 3
http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node18.html
Alex Lopez-Ortiz, University of Waterloo

The movie Pi is featured at http://www.pithemovie.com/.

Fibonacci Numbers and the Golden Ratio

Benjamin, A.T., and J.J. Quinn. 2003. Proofs That Really Count: The Art of Combinatorial Proof. Washington, D.C.: Mathematical Association of America.

Brown, D. 2003. The Da Vinci Code. New York: Doubleday.

Devlin, K. 2004. Cracking the The Da Vinci Code. Discover 25(June).

______. 2004. Good stories, pity they're not true. MAA Online (June). Available at http://www.maa.org/devlin/devlin_06_04.html.

______. 2002. The 800th birthday of the book that brought numbers to the west. MAA Online (October). Available at http://www.maa.org/devlin/devlin_10_02.html.

Elam, K. 2001. Geometry of Design: Studies in Proportion and Composition. New York: Princeton Architectural Press. See http://www.papress.com/books/1568982496.html.

Klar, A.J.S. 2002. Fibonacci's flowers. Nature 417(June 6):595.

Livio, M. 2002. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books.

Markowsky, G. 1992. Misconceptions about the golden ratio. College Mathematics Journal (January). Available at http://www.dur.ac.uk/bob.johnson/fibonacci/miscons.pdf.

Naylor, M. 2002. Golden, sqrt[2], and pi flowers: A spiral story. Mathematics Magazine 75(June):163-172.

Peterson, I. 2004. Counting on Fibonacci. Science News Online (May 1). Available at http://www.sciencenews.org/articles/20040501/mathtrek.asp.

______. 2002. A Fibonacci fountain. Science News Online (Oct. 19). Available at http://www.sciencenews.org/articles/20021019/mathtrek.asp.

______. 2002. Stepping beyond Fibonacci numbers. Science News Online (Sept. 28). Available at http://www.sciencenews.org/articles/20020928/mathtrek.asp.

______. 2002. Golden blossoms and pi flowers. Science News Online (Aug. 31). Available at http://www.sciencenews.org/articles/20020831/mathtrek.asp.

______. 2001. Fibonacci's Chinese calendar. Science News Online (Feb. 3). Available at http://www.sciencenews.org/articles/20010203/mathtrek.asp.

You can learn more of the amazing properties of Fibonacci numbers at http://mathworld.wolfram.com/FibonacciNumber.html.

A biography of Fibonacci can be found at http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Fibonacci.html.

Fibonacci Numbers and the Golden Ratio
http://www.mcs.surrey.ac.uk/Personal.R.Knott/Fibonacci
Ron Knott, Surrey University

Fibonacci Numbers in Nature
http://ccins.camosun.bc.ca/~jbritton/fibslide/jbfibslide.htm
Jill Britton

Phyllotaxis
http://www.math.smith.edu/~phyllo/
Smith College

Galileo and Newton

Crease, R.P. 2003. The legend of the leaning tower. PhysicsWorld (February). Available at http://physicsweb.org/articles/world/16/2/2.

Falling Apple Story
http://www.sfu.ca/physics/ugrad/courses/teaching_resources/demoindex/
mechanics/mech1l/apple.html
Simon Fraser University

Poincaré

Diacu, F. 1996. The solution of the n-body problem. Mathematical Intelligencer 18(No. 3):66-70.

Diacu, F., and P. Holmes. 1996. Celestial Encounters: The Origins of Chaos and Stability. Princeton, N.J.: Princeton University Press.

Gutzwiller, M.C. 1998. Moon-Earth-Sun: The oldest three-body problem. Reviews of Modern Physics 70(April):589.

Holmes, P. 1990. Poincaré, celestial mechanics, dynamical-systems theory and "chaos." Physics Reports 193(September):137.

Morrison, P. 1997. Doing the Poincare shuffle. Scientific American (January):116.

Peterson, I. 1999. Prophet of chaos. Science News Online (Nov. 13). Available at http://www.sciencenews.org/pages/sn_arc99/11_13_99/mathland.htm.

______. 1993. Newton's Clock: Chaos in the Solar System. New York: W.H. Freeman.

The Internet Encyclopedia of Philosophy features a biography of Henri Poincaré at http://www.utm.edu/research/iep/p/poincare.htm. A brief biography also appears at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Poincare.html.

Nobel Prize

Garding, L., L. Hormander. 1985. Why is there no Nobel prize in mathematics? Mathematical Intelligencer 7(No. 3):73-74.

Morrill, J.E. 1995. A Nobel prize in mathematics. Mathematics Magazine (December):888-891.

Ortiz-Lopez, A. 1998. Why is there no Nobel in mathematics? Available at http://db.uwaterloo.ca/~alopez-o/math-faq/node50.html.

Ross, P. 1995. Why isn't there a Nobel prize in mathematics? Math Horizons (November):9. Available at http://mathforum.org/social/articles/ross.html.

Galois and Gauss

Bell, E.T. 1937. Men of Mathematics. New York: Simon & Schuster.

Devlin, K. 1996. Of men, mathematics, and myths. MAA Online (August). Available at http://www.maa.org/devlin/devlin_aug.html.

Dunnington, G.W. 1955. Carl Friedrich Gauss: Titan of Science. New York: Hafner. Reprinted 2004 by the Mathematical Association of America.

Peterson, I. 2004. Young Gauss. Science News Online (Oct. 23). Available at http://www.sciencenews.org/articles/20041023/mathtrek.asp.

______. 1999. The Galois story. Science News Online (Feb. 27). Available at http://www.sciencenews.org/pages/sn_arc99/2_27_99/mathland.htm.

Petsinis, T. 1998. The French Mathematician. New York: Walker.

Rothman, T. 1989. Genius and biographers: The fictionalization of Evariste Galois. In Science a la Mode: Physical Fashions and Fictions. Princeton, N.J.: Princeton University Press. Available at http://godel.ph.utexas.edu/~tonyr/galois.html.

A brief biography of Evariste Galois can be found at http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Galois.html.

A brief biography of Carl Friedrich Gauss can be found at http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Gauss.html.

The Evariste Galois Archive
http://www.galois-group.net/g/EN/links.html

MathZone

Integers

Applegate, D., and J.C. Lagarias. Preprint. Lower bounds for the total stopping time of 3x + 1 interates. Available at http://xxx.lanl.gov/abs/math.NT/0103054.

Dewdney, A.K. 1988. How to pan for primes in numerical gravel. Scientific American 259(July):90-93.

Gardner, M. 1964. The remarkable lore of the prime numbers. Scientific American 210(March):120-128.

Krasikov, I., and J.C. Lagarias. Preprint. Bounds for the 3x + 1 problem using difference inequalities. Available at http://xxx.lanl.gov/abs/math.NT/0205002.

Peterson, I. 2002. Taxicab numbers. Science News Online (July 27). Available at http://www.sciencenews.org/articles/20020727/mathtrek.asp.

______. 2002. Dangerous problems. Science News Online (June 29). Available at http://www.sciencenews.org/articles/20020629/mathtrek.asp.

______. 2002. Prime spirals. Science News Online (May 4). Available at http://www.sciencenews.org/articles/20020504/mathtrek.asp.

______. 2000. The power of partitions. Science News 157(June 17):396-397. Available at http://www.sciencenews.org/articles/20020504/mathtrek.asp.

______. 1997. Winning partitions. Science News Online (March 22). Available at http://www.sciencenews.org/pages/sn_arc97/3_22_97/mathland.htm.

Pickover, C. 1991. A prime plaid. In Computers and the Imagination: Visual Adventures Beyond the Edge. New York: St. Martin's.

Silverman, J.H. 1993. Taxicabs and sums of two cubes. American Mathematical Monthly 100(April):331-340.

Stein, M.L., S.M. Ulam, and M.B. Wells. 1964. A visual display of some properties of the distribution of primes. American Mathematical Monthly 71(May):516-520.

Information about taxicab numbers can be found at http://euler.free.fr/taxicab.htm and http://mathworld.wolfram.com/TaxicabNumber.html.

Pythagoras of Samis: A Collection of Essays and Lessons for Junior and Senior High School
http://www.mathgym.com.au/pythagoras/pythnum.htm

You'll find an introduction to the Collatz (or 3x + 1) problem at http://mathworld.wolfram.com/CollatzProblem.html.

Cliff Pickover's Patterns in the Mysetrious Hailstone (3n + 1) Numbers
http://sprott.physics.wisc.edu/pickover/hailstone.html

Euclidean Geometry

Bergamini, D., and the editors of LIFE. 1963. Mathematics. New York: Time.

Devlin, K. 1998. Life by the Numbers. New York: Wiley.

Peterson, I. 2003. Geometreks. Science News Online (Nov. 8). Available at http://www.sciencenews.org/articles/20031108/mathtrek.asp.

______. 2001. Fragments of Infinity: A Kaleidoscope of Math and Art. New York: Wiley. See http://www.isama.org/book/fragments/.

______. 2000. Puzzling lines. Science News Online (June 10). Available at http://www.sciencenews.org/articles/20000610/mathtrek.asp.

______. 2000. Math trails in Ottawa. Science News Online (May 27). Available at http://www.sciencenews.org/articles/20000527/mathtrek.asp.

Take a virtual tour of the National Gallery of Art's East Building at http://www.nga.gov/collection/eastarch1.htm. Information about I.M. Pei's design can be found at http://www.nga.gov/collection/20th_intro.htm.

Fractals

Friedman, N. 2003. Fractals bounding negative space: Fractal stone prints. Mathematics Awareness Month. Available at http://mathforum.org/mam/03/essay5.html.

Peterson, I. 2003. Fractured granite and fractal prints. Science News Online (April 5). Available at http://www.sciencenews.org/articles/20030405/mathtrek.asp.

______. 2002. Fractal roots and artful math. Science News Online (April 5). Available at http://www.sciencenews.org/articles/20020608/mathtrek.asp.

Hyperbolic Geometry

Henderson, D.W., and D. Taimina. 2001. Crocheting the hyperbolic plane. Mathematical Intelligencer 23(No. 2):17-28.

Peterson, I. 2004. Anatomy of a bead creature. Science News Online (April 17). Available at http://www.sciencenews.org/articles/20040417/mathtrek.asp.

______. 2003. Hyperbolic five. Science News Online (Aug. 30). Available at http://www.sciencenews.org/articles/20030830/mathtrek.asp.

______. 2000. Visions of infinity. Science News 158(Dec. 23&30):408-410.

You can learn more about hyperbolic tilings and art at http://mathforum.org/mam/03/essay1.html.

Additional information about hyperbolic tilings can be found at http://aleph0.clarku.edu/~djoyce/poincare/poincare.html.

You can learn more about the poet William Carlos Williams at http://www.poets.org/poets/poets.cfm?prmID=120. A QuickTime video clip presenting his 1928 poem "The Great Figure" is available at http://www.learner.org/catalog/extras/vvspot/video/williams.html.

Möbius Strips

Burger, E.B., and M. Starbird. 2000. The band that didn't stop playing. In The Heart of Mathematics: An Invitation to Effective Thinking. Emeryville, Calif.: Key College Publishing ( http://www.keycollege.com/Pages/ProdBurger.html).

Fauvel, J., R. Flood, and R. Wilson, eds. 1993. Möbius and his Band: Mathematics and Astronomy in Nineteenth-Century Germany. Oxford, England: Oxford University Press.

Gardner, M. 1989. Möbius bands. In Mathematical Magic Show. Washington, D.C.: Mathematical Association of America.

______. 1956. Mathematics, Magic and Mystery. New York: Dover.

Jones, P., and J. Powell. 1999. Gary Anderson has been found! Resource Recycling (May). Available at http://www.mcmua.com/solidwaste/CreatingtheRecyclingSymbol.htm.

Long, C. 1998. Bug bands and monkey saddles. Math Horizons 5(April):24-28. Available at http://www.wcnet.org/~clong/carving/carving.html.

______. 1996. Möbius or almost Möbius. College Mathematics Journal 27(September):277.

Peterson, I. 2003. Strolling down Möbius lane. Science News Online (Nov. 1). Available at http://www.sciencenews.org/articles/20031101/mathtrek.asp.

______. 2003. Recycling topology. Science News Online (April 26). Available at http://www.sciencenews.org/articles/20030426/mathtrek.asp.

______. 2002. Crystal Möbius. Science News Online (May 25). Available at http://www.sciencenews.org/articles/20020525/mathtrek.asp.

______. 2000. Möbius at Fermilab. Science News Online (Sept. 2). Available at http://www.sciencenews.org/articles/20000902/mathtrek.asp.

______. 2000. Möbius and his band. Science News Online (July 8). Available at http://www.sciencenews.org/20000708/mathtrek.asp.

______. 1999. Möbius in the playground. Science News Online (May 22). Available at http://www.sciencenews.org/pages/sn_arc99/5_22_99/mathland.htm.

A brief biography of August Ferdinand Möbius can be found at http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Mobius.html.

Learn the Afghan bands magic trick at http://www.conjuror.com/magictricks/free_tricks2.html.

Mathematics and Art