Visual Mathematics

 

The official public web page for Math 801-10 : Visual Mathematics
A Dean's Seminar for Freshmen
(This page remains: currently under construction!)

Recommended Visual Math Software:

• Fractint: http://spanky.triumf.ca/www/fractint/fractint.html The classic PC fractal program.Try Winfract MS Windows version.
• Winfeed: http://math.exeter.edu/rparris/winfeed.html A great program that draws many types of fractals
• Tyler:http://www.superliminal.com/geometry/tyler/Tyler.htm, Draws regular and semi-regular tessellations, and more. Web based applet is also available as java appliacation.
• Jeff Week's amazing software including Kali and Kaleidotile :  http://geometrygames.org/
• Tess:  http://www.peda.com/tess/
• Pretzangles: http://www.pretzangles.com/index.html
• Anamorph Me!: http://www.anamorphosis.com  (see also  http://myweb.tiscali.co.uk/artofanamorphosis/AnamorphMe-README.txt )
• QuasiG: http://condellpark.com/kd/quasig.htm A program for drawing Penrose tilings
• Boids: http://www.navgen.com/3d_boids/ Simulation of bird flocking behavior
• Life32:  http://psoup.math.wisc.edu/Life32.html Fully featured program to play Conway's game of Life 
• Life  http://www.robmaeder.com/projects/code/life.php Easy & basic program to play Conway's game of Life 

Artists & Mathematicians:

• Thomas Banchoff: http://www.math.brown.edu/~banchoff/
• Dror Bar-Natan: http://www.math.toronto.edu/~drorbn/Gallery/index.html
• Paul Bourke: http://astronomy.swin.edu.au/~pbourke/
• Brent Collins: http://www.mi.sanu.ac.yu/vismath/col/col1.htm
• Santiago Calatrava: http://www.calatrava.com/
• Bill Casselman: http://www.math.ubc.ca/~cass/
• H. S. M. Coxeter: http://www.math.toronto.edu/coxeter/art-math.html
• Hop David: http://clowder.net/hop/index.html
• Stewart Dixon: http://emsh.calarts.edu/~mathart/portfolio/SPD_Math_portfolio.html
• M. C. Escher: http://www.mcescher.com/
• Robert Fathauer: http://members.cox.net/tessellations/index.html
• Helaman Ferguson:  http://www.helasculpt.com/
• Mike Field: http://nothung.math.uh.edu/~mike/
• R. Buckminster Fuller: http://www.bfi.org/
• Natalie Priebe Frank: http://math.vassar.edu/Faculty/Priebe/default.html
• Nat Friedman: http://math.albany.edu:8000/~artmath/
• Chiam Goodman-Strauss: http://comp.uark.edu/~strauss/
• Alfred Gray: http://www.math.umd.edu/research/bianchi/
• George W. Hart: http://www.georgehart.com/
• Rochelle Newman: http://www.slmm.org/richrochnew/rochnew.html
• Charles Perry: http://www.cs.berkeley.edu/~sequin/SCULPTS/PERRY/
• Marjorie Rice: http://tessellations.home.comcast.net/
• Tony Robbin http://tonyrobbin.home.att.net/
• John Robinson: http://www.cpm.informatics.bangor.ac.uk/sculpture/sculpture.html
• Rudy Rucker: http://www.mathcs.sjsu.edu/faculty/rucker/
• Brian Sanderson: http://www.maths.warwick.ac.uk/~bjs/
• Lana Schneider: http://fiberarts.org/design/articles/algebra.html
• Lillian F. Schwartz: http://www.lillian.com/
• Richard Evan Schwartz: http://www.math.brown.edu/~res/
• Henry Segerman: http://www.stanford.edu/~segerman/
• Carlo Sequin: http://www.cs.berkeley.edu/~sequin/
• Koos Verheoff: http://www.arsetmathesis.nl/verhoeff.htm
• Stan Wagon: http://www.stanwagon.com/
• Matthias Weber: http://www.math.uni-bonn.de/people/weber/
• Jeff Weeks: http://geometrygames.org/

Online Art Galleries:

Hands on Math: http://geometrygames.org/
Anamorphosis: http://www.anamorphosis.com/
World of Mathematics (by Eric Weissstein):  http://mathworld.wolfram.com/topics/MathematicalArt.html

Pages on topics of interest:

• The book Flatland on-line: http://www.alcyone.com/max/lit/flatland/
• Polyhedra
• Paper Models of Polyhedra: http://www.korthalsaltes.com/
• 
  
• Tilings of squares by squares: http://www.maa.org/editorial/mathgames/mathgames_12_01_03.html
• Math in the movies: http://world.std.com/~reinhold/dir/mathmovies.html
• Architecture
• Federation Square in Australia: http://www.fedsq.com/

Surveys of Math and Art:

American Mathematical Society: http://www.ams.org/new-in-math/cover/art1.html

University of Greifswald (in German):  http://www.math-inf.uni-greifswald.de/mathematik+kunst/
Other "Math & Art"  Courses:

• Dartmouth University: http://www.math.dartmouth.edu/~matc/
• Indiana University: http://mypage.iu.edu/~mathart/viewpoints/lessons/

Bibliography:

·         Edwin Abbott Abbott, Flatland, Signet, 1994 (Note: Text now available online)

·        Thomas Banchoff, Beyond the Third Dimension: Geometry, Computer Graphics and Higher Dimensions,  Scientific American Library, 1996, (Gelman QA 691 .B26 1996).

·        Michael Barnsley, Fractals Everywhere (2^nd Ed.), Academic Press, 1993.

·       Edward Berger and Michael Starbird, The Heart of Mathematics, Key College Publishing, 2000,

·        Claud P. Bruter (ed), Mathematics and Art: Mathematics and Visualization in Art and Education , Springer Verlag, 2002 (Gelman:  NX 180 .M33 M35 2002).

·        COMAP group, For All Practical Purposes (2^nd Ed), W. H. Freeman, 1988.

·       György Doczi, The power of Limis: Proportional Harmonies in Nature Art and Architecture, Shambhala Pub. Inc., 1981.

·       Richard A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific, 1997, (Gelman: QA466.D86 1997).

·        Ron Eglash, African Fractals, Rutgers University Press, 1999 (AU GN 650 .E35 1999)

·        Michele Emmer, The Visual Mind: Art and Mathematics, MIT Press, 1995 (Mt. Vernon, N 72 .M3 V58 1993).

·       Peter Engel, Origami from Angelfish to Zen, Dover , 1989.

·         M. :L. Frame & B. B. Mandelbrodt, Fractals, Graphics & Mathematics Education, MAA Press. 2002 (Gelman QA 614.86 .F68434 2002)

·     George Gamow, One, Two, Three...Infinity, Bantum, 1969.

·        Lynn Gamwell, Exploring the Invisible: Art, Science and the Spriitual, Princeton University Press, 2002 (Gelman: N 72 .S3 G36 2002).

·        Branko Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, 1978

·        Jaques Hasamard, The Mathematician's Mind, Princeton University Press, 1945, 1996 (Gelman: QA 8.4 .H3 1996)

·       István Hargittai and Magdolna Hargittai, Symmetry: A Unifying Concept, Shelter Publications, 1994.

·       István Hargittai (Ed.), Fivefold Symmetry, World Scientific, 1992, Q172.5 F58 1992.

·       István Hargittai and Clifford Pickover (Ed.), Spiral Symmetry, World Scientific, 1992.

·       Linda Dalrymple Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, Princeton University Press, 1983,  N 6490.H44 1983.

·       Douglas R. Hofstadter, Gödel, Escher, Bach, Vintage Books, 1979.

·        Robert D. Huerta, Giants of Delft, Associated University Press, 2003 (Gelman N 72 .S3 H84, 2003).

·        William M. Ivans, Jr., Art & Geometry, Dover, 1964 (Gelman N 76 .I9 1964)

·       Paul Johnson, Art: A new History, Harper Collins, 2003.

·       R. Stanley Johnson, Cubism & la Section d’Or, Klees/Gustorf Publishers, 1991, N 6494.C8 J63 1991

·       L. Christine Kinsey and Teresa E. Moore, Symmetry, Shape and Space, Key College Publishing, 2002

·       Hans Meinhardt, The Algorithmic Beauty of Sea Shells, Springer-Verlag, 1995.

·       Arthur I. Miller, Einstein Picasso, Basic Books, 2001, N72.S3 M55 2001

·        James R. Newman, The Works of Mathematics (V 1-4), Simon and Shuster, 1956

·       David Mumford, Caroline Series and David Wright, Indra’s Pearls, Cambridge U. Press, 2002.

·       Hanz-Otto Peitgen, Hartmut Jürgens, and Dietmar Saupe, Fractals for the Classroom, Springer Verlag, 1992 (Gelman QA 614.86 .p45 1992 v.1).

·       Przemyslaw Prusinkeiwicz and Aristid Lindenmayer, The Algorithmic Beauty of Plants, Springer-Verlag, 1990.

·       John Adkins Richardson, Modern Art and Scientific Thought, University of Illinois Press, 1971, N 72.S3R5

·       Tony Robbin, fourfield: Computers, Art & the 4^th Dimension, 1992.

·       Rudy Rucker, 4^th Dimension, Houghton Mifflin, 1984.

·       Rudy Rucker, Spaceland, Tim Doherrty Associates, LLC, 2002.

·       Michael Serra, Discovering Geometry , Key Curriculum Press, 1993.

·       Lynn Arthur Steen (Ed.), On the Shoulders of Giants , National Academy Press,

·       Ian Stewart, Flatterland, Pegasus Publishing, 2001.

·        Eliane Strosberg, Art and Science, Abeville Press Publishers, 1999 (Gelman: N 72 .S3 S77 2001)

·       Peter Tannenbaum, Excursions in Modern Mathematics (5^th Ed), Prentice Hall, 2003

·       Jeffrey R. Weeks, The Shape of Space, Marcel Dekker, Inc., 1985, QA612.12 .W44 1985