Bibliography: Fragments of Infinity

 

 Fragments of Infinity: A Kaleidoscope of Math and Art

By Ivars Peterson

Updated Bibliography (with Web Links)

  • General Bibliography

  • Gallery Visits
  • Theorems in Stone
  • A Place in Space
  • Plane Folds
  • Grid Fields
  • Crystal Visions
  • Strange Sides
  • Minimal Snow
  • Points of View
  • Fragments

  • Corrections and Clarifications

  • Additional Artists and Resources


General Bibliography

Albers, Donald J., and G. L. Alexanderson, eds. 1985. Mathematical People: Profiles and Interviews. Boston: Birkhäuser.

Albers, Donald J., Gerald L. Alexanderson, and Constance Reid, eds. 1990. More Mathematical People: Contemporary Conversations. San Diego, Calif.: Academic Press.

Burger, Edward B., and Michael Starbird. 2000. The Heart of Mathematics: An Invitation to Effective Thinking. Emeryville, Calif.: Key College Publishing.

Devlin, Keith. 2000. The Language of Mathematics: Making the Invisible Visible. New York: W. H. Freeman.

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

Hilton, Peter, Derek Holton, and Jean Pedersen. 1997. Mathematical Reflections: In a Room with Many Mirrors. New York: Springer.

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

Peterson, Ivars. 1990. Islands of Truth: A Mathematical Mystery Cruise. New York: W. H. Freeman.

Sarhangi, Reza, and Slavik Jablan, eds. 2001. Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings. See http://www.sckans.edu/~bridges/.

Sarhangi, Reza, ed. 2000. Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings. See http://www.sckans.edu/~bridges/ .

Sarhangi, Reza, ed. 1999. Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings. See http://www.sckans.edu/~bridges/ .

Sarhangi, Reza, ed. 1998. Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings. See http://www.sckans.edu/~bridges/ .

Steen, Lynn Arthur, ed. 1990. On the Shoulders of Giants: New Approaches to Numeracy. Washington, D. C.: National Academy Press.


Nexus Network Journal:
http://www.nexusjournal.com/
Visual Mathematics:
http://members.tripod.com/vismath/
YLEM: Artists Using Science and Technology:
http://www.ylem.org/

Chapter 1. Gallery Visits

Bliss, Anna Campbell. 1999. Architectural extents. In First Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture (ISAMA 99), Nathaniel Friedman and Javier Barrallo, eds. San Sebastián, Spain: University of the Basque Country.

Emmer, Michele, ed. 1995. The Visual Mind: Art and Mathematics. Cambridge, Mass.: MIT Press.

Field, J. V. 1997. The Invention of Infinity: Mathematics and Art in the Renaissance. New York: Oxford University Press.

Friedman, Nathaniel, and Javier Barrallo. 1999. First Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture (ISAMA 99). San Sebastián, Spain: University of the Basque Country.

Gardner, Martin. 2001. Infinite regress, In The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton.

Gardner, Martin. 1992. Minimal sculpture. In Fractal Music, Hypercards and More. . .Mathematical Recreations from Scientific American Magazine. New York: W. H. Freeman.

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

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

Kapraff, Jay. 1991. Connections: The Geometric Bridge between Art and Science. New York: McGraw-Hill.

Peterson, Ivars. 2000. ISAMA 2000. Nexus Network Journal 2: 211-213. Available at http://www.nexusjournal.com/conf_reps_v2n4-Peterson.html .

Peterson, Ivars. 2000. Mathematical art on display. Science News Online (Nov. 4). Available at http://www.sciencenews.org/20001104/mathtrek.asp .

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

Peterson, Ivars. 1999. Geometry out of Africa. Science News Online (Nov. 27). Available at http://www.sciencenews.org/sn_arc99/11_27_99/mathland.htm .

Peterson, Ivars. 1999. Jackson Pollock's fractals. Science News Online (Sept. 18). Available at http://www.sciencenews.org/sn_arc99/9_18_99/mathland.htm .

Singer, Clifford. 2000. On visual mathematics in art. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Singer, Clifford. 1999. The conceptual mechanics of expression in geometric fields. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. Available at http://members.tripod.com/vismath/clif/index.html.

Singer, Clifford. 1999. Geometrical fields. In First Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture (ISAMA 99), Nathaniel Friedman and Javier Barrallo, eds. San Sebastián, Spain: University of the Basque Country.


Anna Campbell Bliss:
http://wwol.inre.asu.edu/bliss.html
Nat Friedman:
http://www.albany.edu/~artmath/
George Hart:
http://www.georgehart.com/
Piet Mondrian:
http://www.artchive.com/artchive/ftptoc/mondrian_ext.html
Henry Moore:
http://www.henry-moore-fdn.co.uk/hmf/
Clifford Singer:
http://math.rice.edu/~joel/NonEuclid/singer/
Kenneth Snelson:
http://www.grunch.net/snelson/
Koos Verhoeff:
http://wwwpa.win.tue.nl/wstomv/math-art/koos/tue-9809/

Chapter 2. Theorems in Stone

Albers, D. 1994. Carving mathematics. Math Horizons (November): 14-17.

Cannon, J. W. 1991. Mathematics in marble and bronze: The sculpture of Helaman Rolfe Pratt Ferguson. Mathematical Intelligencer 13 (No. 1): 30.

Cipra, Barry A. 1997. Quod granite demonstrandum. SIAM News 30 (December): 1.

Cipra, Barry A. 1990. Mathematical ideas shape sculptor's work. SIAM News 23 (May): 24.

Ferguson, Claire. 1994. Helaman Ferguson: Mathematics in Stone and Bronze. Erie, Penn.: Meridian Creative Group.

Ferguson, Helaman. 1999. Duality in mathematical sculpture: Linking Klein bottles in granite. International Journal of Shape Modeling 5 (No. 1): 55-68.

Ferguson, Helaman. 1999. Equations to stone sculpture. In First Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture (ISAMA 99), Nathaniel Friedman and Javier Barrallo, eds. San Sebastián, Spain: University of the Basque Country.

Ferguson, Helaman. 1993. Computer interactive sculpture. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Ferguson, Helaman. 1990. Two theorems, two sculptures, two posters. American Mathematical Monthly 97 (August-September): 589-610.

Gardner, Martin. 2001. Klein bottles and other surfaces. In The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton.

Peterson, Ivars. 2001. Immersed in Klein bottles. Science News Online (Feb. 17). Available at http://www.sciencenews.org/20010217/mathtrek.asp .

Peterson, Ivars. 1996. The song in the stone. Science News 149 (Feb. 17): 110-112.

Peterson, Ivars. 1990. Equations in stone. Science News 138 (Sept. 8): 152-154.

Stewart, Ian. 1998. Glass Klein bottles. Scientific American279 (March):101.


Helaman Ferguson:
http://www.helasculpt.com/
John Sullivan:
http://www.math.uiuc.edu/~jms/
http://members.tripod.com/vismath4/sul/sul.htm

Chapter 3. A Place in Space

Abbott, Edwin A. 1884. Flatland: A Romance of Many Dimensions by A Square. London: Seeley & Co.

Albers, D. J. 1996. Tom Banchoff: Multidimensional mathematician. Math Horizons (February): 18-22.

Asimov, Daniel. 1995. There's no space like home. The Sciences (September-October): 20-25.

Banchoff, Thomas, and Davide Cervone. 1993. Illustrating Beyond the Third Dimension. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Banchoff, Thomas F. 1990. Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions. style="mso-spacerun: yes"> New York: Scientific American Library.

Brisson, Harriet E. 1999. Aesthetic geometry. In First Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture (ISAMA 99), Nathaniel Friedman and Javier Barrallo, eds. San Sebastián, Spain: University of the Basque Country.

Brisson, Harriet E. 1993. Visualization in art and science. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Coxeter, H. S. M. 1973. Regular Polytopes, 3rd. ed. New York: Dover.

Dewdney, A. K. 1986. A program for rotating hypercubes induces four-dimensional dementia. Scientific American (April): 14-23.

Gardner, Martin. 2001. The church of the fourth dimension. In The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton.

Gardner, Martin. 2001. The wonders of a planiverse. In The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton.

Gardner, Martin. 1989. Hypercubes. In Mathematical Carnival. Washington, D. C.: Mathematical Association of America.

Gardner, Martin. 1969. Flatlands. In The Unexpected Hanging and Other Mathematical Diversions. New York: Simon and Schuster.

Henderson, Linda Dalrymple. 1998. Duchamp in Context: Science and Technology in the Large Glass and Related Works. Princeton, N. J.: Princeton University Press.

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

Kemp, Martin. 1998. Dalí's dimensions. Nature 391 (Jan. 1): 27.

Ouspensky, P. D. 1997. A New Model of the Universe: Principles of the Psychological Method in Its Application to Problems of Science, Religion, and Art. Mineola, N. Y.: Dover.

Peterson, Ivars. 2000. A stranger from spaceland. Science News Online (Jan. 1). Available at http://www.sciencenews.org/20000101/mathtrek.asp .

Peterson, Ivars. 1984. Shadows from a higher dimension. Science News 126 (Nov. 3): 284-285.

Pickover, Clifford A. 1999. Surfing Through Hyperspace: Understanding Higher Universes in Six Easy Lessons. New York: Oxford University Press.

Rucker, Rudy. 1984. The Fourth Dimension: Toward a Geometry of Higher Reality. New York: Houghton Mifflin.

Shlain, Leonard. 1991. Art & Physics: Parallel Visions in Space, Time, and Light. New York: William Morrow.

Stewart, Ian. 2001. Flatterland: Like Flatland, Only More So. Cambridge, Mass.: Perseus Publishing.

Stewart, Ian. 1995. One hundred and one dimensions. New Scientist (Oct. 11): 28-31.


Thomas Banchoff:
http://www.math.brown.edu/~banchoff/art/
http://www.math.brown.edu/~banchoff/
Harriet Brisson:
http://www.ilpi.com/artsource/vce/brisson.html
http://www.ric.edu/bannister/IMAGES/JUNE96/Brisson.html
Davide P. Cervone:
http://www.math.union.edu/~dpvc/professional/art/welcome.html
Salvador Dali:
http://www.artchive.com/artchive/ftptoc/dali_ext.html
A hyperspace tutorial can be found at:
http://www.uccs.edu/~eswab/hyprspac.htm

Chapter 4. Plane Folds

Cipra, Barry. 1998. Algorigami, anyone? Science 279 (Feb. 6): 805.

Demaine, Erk D., Martin L. Demaine, and Anna Lubiw. 1999. Polyhedral sculptures with hyperbolic paraboloids. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Gardner, Martin. 1996. The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays. New York: Copernicus.

Gardner, Martin. 1989. Pascal's triangle. In Mathematical Carnival. Washington, D. C.: Mathematical Association of America.

Gardner, Martin. 1961. Origami. In The 2nd Scientific American Book of Mathematical Puzzles & Diversions. New York: Simon and Schuster.

Gurkewitz, Rona, and Bennett Arnstein. 1995. 3-D Geometric Origami: Modular Polyhedra. New York: Dover.

Lang, Robert J. 1997. Origami in Action: Paper Toys that Fly, Flap, Gobble, and Inflate! New York: St. Martin's Griffin.

Lang, Robert J. 1997. The tree method of origami design. In Origami Science & Art: Proceedings of the Second International Meeting of Origami Science and Scientific Origami, Koryo Miura, ed. Otsu, Japan: Seian University of Art and Design.

Lang, Robert J. 1996. A computational algorithm for origami design. In Proceedings of the 12th Annual ACM Symposium on Computational Geometry. New York: Association for Computing Machinery.

Miura, Koryo, ed. 1997. Origami Science & Art: Proceedings of the Second International Meeting of Origami Science and Scientific Origami. Otsu, Japan: Seian University of Art and Design.

Montroll, John. 1998. Teach Yourself Origami. New York: Dover.

Neale, Robert, Thomas Hull, and Lionel Delevingne. 1994. Origami, Plain and Simple. New York: St. Martin's Press.

Peterson, Ivars. 1999. Plane patterns. Science News Online (March 13). Available at http://www.sciencenews.org/sn_arc99/3_13_99/mathland.htm .

Peterson, Ivars. 1995. Crinkled doughnuts. Science News 148 (Dec. 23&30): 432-433.

Stewart, Ian. 1999. Origami tessellations. Scientific American 280 (February): 100-101.

Verrill, Helena. 1998. Origami tessellations. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .


Erik Demaine:
http://db.uwaterloo.ca/~eddemain/
Thomas Hull:
http://web.merrimack.edu/~thull/
Robert J. Lang:
http://www.origami.vancouver.bc.ca/Gallery/other.html
Chris K. Palmer:
http://www.shadowfolds.com/
Helena Verrill:
http://hverrill.net/pages~helena/origami/
Illustrations of Helena Verrill's Pascal triangle unit and its construction can be found at:
http://hverrill.net/pages~helena/origami/pascal/
http://modular.fas.harvard.edu/hverrill/photos/pascal-unit/
Instructions for the square twist pattern can be found at:
http://hverrill.net/pages~helena/origami/tessellations/squaretwist/
Joseph Wu's origami page:
http://origami.vancouver.bc.ca/

Chapter 5. Grid Fields

Blatner, David. 1997. The Joy of p New York: Walker.

Crutchfield, James P., J. Doyne Farmer, Norman H. Packard, and Robert Shaw. 1986. Chaos. Scientific American 255 (December): 46-57.

Dewdney, A. K. 1986. Wallpaper for the mind: Computer images that are almost, but not quite, repetitive. Scientific American 255 (September): 14-23.

Dewdney, A. K. 1986. A computer microscope zooms in for a look at the most complex object in mathematics. Scientific American 255 (August): 16-24.

Gardner, Martin. 1995. The transcendental number pi. In New Mathematical Diversions. Washington, D.C.: Mathematical Association of America.

Gardner, Martin. 1989. Mandelbrot's fractals. In Penrose Tiles to Trapdoor Ciphers. New York: W. H. Freeman.

Gardner, Martin. 1988. Anamorphic art. In Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman.

Gardner, Martin. 1969. Rep-tiles: Replicating figures on the plane. In The Unexpected Hanging and Other Mathematical Diversions. New York: Simon and Schuster.

Mandelbrot, Benoit B. 1993. Fractals and art for the sake of science. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Mandelbrot, Benoit B. 1983. The Fractal Geometry of Nature. New York: W. H. Freeman.

Field, Michael, and Martin Golubitsky. 1995. Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature. New York: Oxford University Press.

McGuire, Michael. 1991. An Eye for Fractals: A Graphic & Photographic Essay by Michael McGuire. Reading, Mass.: Addison-Wesley.

Peden, Douglas D. 1998. Bridges of mathematics, art, and physics. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. Available at http://members.tripod.com/vismath5/pedens/index.html .

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

Peterson, Ivars. 2001. Art of pursuit. Science News Online (July 21). Available at http://www.sciencenews.org/20010721/mathtrek.asp style='font-size:10.0pt'>.

Peterson, Ivars. 2001. Pursuing pursuit curves. Science News Online (July 21). Available at http://www.sciencenews.org/20010714/mathtrek.asp .

Peterson, Ivars. 2000. Scrambled grids. Science News Online (Aug. 26). Available at http://www.sciencenews.org/20000826/mathtrek.asp .

Peterson, Ivars. 2000. Art of the grid. Science News Online (Aug. 12). Available at http://www.sciencenews.org/20000812/mathtrek.asp .

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

Pickover, Clifford A., ed. 1995. The Pattern Book: Fractals, Art, and Nature. Singapore: World Scientific.

Pickover, Clifford A. 1995. Keys to Infinity. New York: Wiley.

Pickover, Clifford A. 1992. Mazes for the Mind: Computers and the Unexpected. New York: St. Martin's Press.

Pickover, Clifford A. 1991. Computers and the Imagination: Visual Adventures Beyond the Edge. New York: St. Martin's Press.

Pickover, Clifford A. 1990. Computers, Pattern, Chaos and Beauty: Graphics from an Unseen World. New York: St. Martin's Press.

Stewart, Ian. 1989. Does God Play Dice? The Mathematics of Chaos. Cambridge, Mass.: Basil Blackwell.


Bob Brill:
http://users.migate.net/~bobbrill/
Mike Field:
http://nothung.math.uh.edu/~mike/
http://members.tripod.com/vismath6/field/index.html
Douglas Peden:
http://members.tripod.com/vismath6/peden/index.html
Arlene Stamp:
http://www.ccca.ca/artists/stamp.html

Chapter 6. Crystal Visions

Gardner, Martin. 1989. Penrose tiling. In Penrose Tiles to Trapdoor Ciphers. New York: W. H. Freeman.

Gardner, Martin. 1989. Penrose tiling II. In Penrose Tiles to Trapdoor Ciphers. New York: W. H. Freeman.

Gardner, Martin. 1988. Tiling with convex polygons. In Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman.

Gailiunas, Paul. 2000. Spiral tilings. In Bridges: Mathematical Connections in Art, Music, and Science, Sarhangi, Reza, ed. Available at http://members.tripod.com/vismath4/gal/index.html .

Gardner, Martin. 2001. Rep-tiles. In The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton.

Gardner, Martin. 2001. Penrose tiles. In The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton.

Grünbaum, Branko, and G. C. Shephard. 1987. Tilings and Patterns. New York: W. H. Freeman.

La Breque, Mort. 1987. Opening the door to forbidden symmetries. Mosaic 18 (Winter): 2-23.

Nelson, David R. 1986. Quasicrystals. Scientific American 255 (August): 42-51.

Penrose, Roger. 1993. On the cohomology of impossible figures. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Penrose, Roger. 1989. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. New York: Oxford University Press.

Peterson, Ivars. 1996. Clusters and decagons. Science News 150 (Oct. 12): 232-233. Available at http://www.sciencenews.org/sn_arch/10_12_96/bob1.htm .

Peterson, Ivars. 1991. Shadows and symmetries. Science News 140 (Dec. 21/28): 408-410.

Peterson, Ivars. 1988. Tiling to infinity. Science News 134 (July 16): 42.

Peterson, Ivars. 1985. The fivefold way for crystals. Science News 127 (March 23): 188-189.

Peterson, Ivars. 1979. Pentaplexity: A class of non-periodic tilings of the plane. Mathematical Intelligencer 2 (No. 1): 32-37.

Robbin, Tony. 1996. Engineering a New Architecture: How New Engineering Materials and Techniques are Influencing Architectural Design. New Haven, Conn.: Yale University Press.

Robbin, Tony. 1992. Fourfield: Computers, Art, and the Fourth Dimension. Boston: Little, Brown and Company.

Robbin, Tony. 1984. Painting and physics: Modeling artistic and scientific experience in four spatial dimensions. Leonardo 17 (No. 4): 227-233.

Peterson, Ivars. 1999. Coloring Penrose tiles. Science News Online (May 15). Available at http://www.sciencenews.org/sn_arc99/5_15_99/mathland.htm .

Schattschneider, Doris. 1998. In praise of amateurs. In Mathematical Recreations: A Collection in Honor of Martin Gardner, David A. Klarner, ed. Mineloa, N. Y.: Dover.

Schattschneider, Doris. 1993. The fascination of tiling. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Senechal, Marjorie. 1995. Quasicrystals and Geometry. Cambridge, England: Cambridge University Press.

Steinhardt, Paul Joseph. 1986. Quasicrystals. American Scientist 74 (November/December): 586-597.

Venters, Diana, and Elaine Krajenke Ellison. 1999. Mathematical Quilts: No Sewing Required! Emeryville, Calif.: Key Curriculum Press.


Eleni Mylonas:
http://www.elenimylonas.com/
Tony Robbin:
http://TonyRobbin.home.att.net/

Chapter 7. Strange Sides

Barr, Stephen. 1989. Experiments in Topology. New York: Dover.

Bill, Max. 1993. The mathematical way of thinking in the visual art of our time. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Brown, Ronald. 1999. John Robinson's symbolic sculptures, knots and mathematics. In First Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture (ISAMA 99), Nathaniel Friedman and Javier Barrallo, eds. San Sebastián, Spain: University of the Basque Country.

Emmer, Michele. 2000. Mathematics and art: Bill and Escher. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Fauvel, John, Raymond Flood, and Robin Wilson, eds. 1993. Möbius and His Band: Mathematics and Astronomy in Nineteenth-Century Germany. New York: Oxford University Press.

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

Isaksen, Daniel C., and Alabama P. Petrofsky. 1999. Möbius knitting. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Perry, Charles O. 1998. Continuum, broken symmetry, and more. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Perry, Charles O. 1993. On the edge of science: The role of the artist's intuition in science. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Peterson, Ivars. 2001. Möbius accordion. Science News Online (June 9). Available at http://www.sciencenews.org/20010609/mathtrek.asp .

Peterson, Ivars. 2001. Möbius at Fermilab. Science News Online (Sept. 2). Available at http://www.sciencenews.org/20000902/mathtrek.asp .

Peterson, Ivars. 2001. Möbius and his band. Science News Online (July 8). Available at http://www.sciencenews.org/20000708/mathtrek.asp .

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

Peterson, Ivars. 1996. Recycling topology. Science News Online (Sept. 28). Available at http://www.sciencenews.org/sn_arch/9_28_96/mathland.htm .

Séquin, Carlo H. 2000. ". . .to build a twisted bridge. . ." In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .


Max Bill:
http://www.cpm.informatics.bangor.ac.uk/sculmath/mb.htm
Benigna Chilla:
http://members.tripod.com/vismath5/benigna/
Charles O. Perry:
http://www.charlesperry.com/
http://members.tripod.com/vismath6/perry/index.html
John Robinson:
http://www.cpm.informatics.bangor.ac.uk/sculmath/
http://members.tripod.com/vismath/exrob/index.html
Keizo Ushio:
http://www2.memenet.or.jp/~keizo/
http://www.cs.berkeley.edu/~sequin/SCULPTS/KEIZO/
http://www.cs.berkeley.edu/~sequin/SFF/FDM_parts/fdm_keizo.html

Chapter 8. Minimal Snow

Bruning, John, Andy Cantrell, Robert Longhurst, Dan Schwalbe, and Stan Wagon. 2000. Rhapsody in White: A victory of mathematics. Mathematical Intelligencer 22 (No. 4): 37-40.

Dickson, Stewart. 1993. True 3D computer modeling: Sculpture of numerical abstraction. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Gray, Alfred. 1998. Modern Differential Geometry of Curves and Surfaces with Mathematica®, 2nd. ed. Boca Raton, Fla.: CRC Press.

Hildebrandt, Stefan, and Anthony Tromba. 1996. The Parsimonious Universe: Shape and Form in the Natural World. New York: Springer-Verlag.

Hoffman, David, and William H. Meeks, III. 1990. Minimal surfaces based on the catenoid. American Mathematical Monthly 97 (October): 702-730.

Peterson, Ivars. 2001. White narcissus. Science News Online (Feb. 10). Available at http://www.sciencenews.org/20010210/mathtrek.asp .

Peterson, Ivars. 2000. A minimal winter's tale. Science News Online (Feb. 5). Available at http://www.sciencenews.org/20000205/mathtrek.asp .

Peterson, Ivars. 1999. Minimal snow. Science News Online (March 6). Available at http://www.sciencenews.org/sn_arc99/3_6_99/mathland.htm .

Peterson, Ivars. 1992. Putting a handle on minimal helicoids. Science News 142 (Oct. 24): 276.

Peterson, Ivars. 1985. Three bites in a doughnut. Science News 127 (March 16): 168-169.


Stewart Dickson:
http://emsh.calarts.edu/~mathart/SPD_ref.html
David Hoffman:
http://www.msri.org/publications/sgp/SGP/
Robert Longhurst:
http://www.cs.berkeley.edu/~sequin/SCULPTS/LONGHURST/

Chapter 9. Points of View

Adams, Colin C. 2001. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman.

Casselman, Bill. 2000. Pictures and proofs. Notices of the American Mathematical Society 47 (November): 1257-1266.

Collins, Brent. 2001. Geometries of curvature and their aesthetics. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, and Slavik Jablan, eds. Available at http://members.tripod.com/vismath6/collins1/index.html .

Collins, Brent. 2000. Visualization: From biology to culture. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Collins, Brent. 1999. Merging paradigms. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Collins, Brent. 1998. Finding an integral equation of design and mathematics. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Collins, Brent. 1997. Evolving an aesthetic of surface economy in sculpture. Leonardo 30 (No. 2): 85-88.

Collins, Brent. 1993. Topological sculptures. Interdisciplinary Science Reviews 18 (No. 1): 9-12.

Cox, Donna J. 1993. Caricature, readymades and metamorphosis: Visual mathematics in the context of art. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Francis, George K. 1987. A Topological Picturebook. New York: Springer-Verlag.

Francis, George K., and Brent Collins. 1992. On knot-spanning surfaces: An illustrated essay on topological art. With an artist's statement by Brent Collins. Leonardo 25 (No. 3/4): 313-320.

Friedman, Nathaniel A. 2001. Knots and multiple Möbius band minimal surfaces. Visual Mathematics 3 (No. 2). Available at http://members.tripod.com/vismath6/friedman1/index.html .

Friedman, Nathaniel A. 2000. What do you see? In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Friedman, Nathaniel A. 1999. Geometric sculpture for K-12: Geos, hyperseeing, and hypersculpture. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Friedman, Nathaniel A. 1999. Form, space, and light. In First Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture (ISAMA 99), Nathaniel Friedman and Javier Barrallo, eds. San Sebastián, Spain: University of the Basque Country.

Friedman, Nathaniel A. 1998. Hyperseeing, hypersculptures and space curves. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. Available at http://members.tripod.com/vismath5/friedman/index.html .

Gardner, Martin. 2001. Knots. In The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton.

Gardner, Martin. 1997. The topology of knots. In The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications. New York: Copernicus.

Gardner, Martin. 1986. Worm paths. In Knotted Doughnuts and Other Mathematical Entertainments. New York: W. H. Freeman.

Gardner, Martin. 1961. The five Platonic solids. In The Second Scientific American Book of Mathematical Puzzles and Diversions. New York: Simon and Schuster.

Krawczyk, Robert J. 2001. Curving spirolaterals. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, and Slavik Jablan, eds. See http://www.sckans.edu/~bridges/ .

Krawczyk, Robert J. 2001. More curved spirolaterals. Visual Mathematics 3 (No. 2). Available at http://members.tripod.com/vismath6/kraw/index.html .

Krawczyk, Robert A. 1999. Spirolaterals, complexity from simplicity. In First Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture (ISAMA 99), Nathaniel Friedman and Javier Barrallo, eds. San Sebastián, Spain: University of the Basque Country.

Levine, Howard. 1997. See-duction: How scientists and artists are creating a third way of knowing. Humanistic Mathematics Network Journal (No. 15): 41-45.

Moretti, Ugo. 1984. Carlo Roselli. Rome: Edizioni S. I. R. I. S.

Peterson, Ivars. 2000. Turtle tracks. Science News Online (July 22). Available at http://www.sciencenews.org/20000722/mathtrek.asp .

Peterson, Ivars. 2000. Punctured polyhedra. Science News Online (June 17). Available at http://www.sciencenews.org/20000617/mathtrek.asp .

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

Peterson, Ivars. 1999. Art of the tetrahedron. Science News Online (Nov. 6). Available at http://www.sciencenews.org/sn_arc99/11_6_99/mathland.htm .

Peterson, Ivars. 1999. Sculpture generator. Science News Online (Oct. 2). Available at http://www.sciencenews.org/sn_arc99/10_2_99/mathland.htm .

Peterson, Ivars. 1998. Twists through space. Science News 154 (Aug. 29): 143.

Peterson, Ivars. 1991. Plastic math. Science News 140 (Aug. 3): 72-73.

Séquin, Carlo H. 1999. Analogies from 2D to 3D: Exercises in disciplined creativity. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. Available at http://members.tripod.com/vismath4/sequin/index.html .

Séquin, Carlo H. 1999. Computer-augmented inspiration. In First Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture (ISAMA 99), Nathaniel Friedman and Javier Barrallo, eds. San Sebastián, Spain: University of the Basque Country.

Séquin, Carlo H. 1998. Art, math, and computers: New ways of creating pleasing shapes. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Wenninger, Magnus J. 1971. Polyhedron Models. London, England: Cambridge University Press.


Brent Collins:
http://http.cs.berkeley.edu/~sequin/SCULPTS/collins.html
http://www.cs.berkeley.edu/~sequin/SCULPTS/scherk.html
http://www.sckans.edu/~bridges/bcollins/bcollins.html
George Francis:
http://www.math.uiuc.edu/~gfrancis/
Robinson Fredenthal:
http://www.upenn.edu/gsfa/rf/aboutrf.html
Charles Ginnever:
http://www.base24.com/gallery/GINNEVER/gin2.htm
Bathsheba Grossman:
http://www.bathsheba.com/
Robert J. Krawczyk:
http://home.netcom.com/~bitart/mathtrek.htm#3
http://members.tripod.com/vismath6/krawczyk/index.htm
Sol LeWitt:
http://www.crownpoint.com/artists/lewitt/
Carlo Séquin:
http://http.cs.berkeley.edu/~sequin/SCULPTS/sequin.html
http://members.tripod.com/vismath4/seq/index.html
Arthur Silverman:
http://www.neworleansonline.com/culture/Silverman.shtml

Chapter 10. Fragments

Coxeter, H. S. M. 1998. Angels and devils. In Mathematical Recreations: A Collection in Honor of Martin Gardner, David A. Klarner, ed. Mineloa, N. Y.: Dover.

Coxeter, H. S. M. 1961. Introduction to Geometry. New York: Wiley.

Coxeter, H. S. M., M. Emmer, R. Penrose, and M. L. Teuber, eds. 1986. M. C. Escher Art and Science: Proceedings of the International Congress on M. C. Escher, Rome, Italy, 26-28 March, 1985. Amsterdam: North-Holland.

Dunham, Douglas. 2000. Hyperbolic Celtic knot patterns. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Dunham, Douglas. 1999. Artistic patterns in hyperbolic geometry. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Dunham, Douglas. 1999. Transformation of hyperbolic Escher patterns. Visual Mathematics 1 (No. 1). Available at http://members.tripod.com/vismath/dunham/index.html .

Escher, M. C. 2000. The Magic of M. C. Escher. New York: Abrams.

Escher, M. C. 1967. The Graphic Work of M. C. Escher. New York: Meredith Press.

Gardner, Martin. 2001. Non-Euclidean geometry. In The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W. W. Norton.

Gardner, Martin. 1995. H. S. M. Coxeter. In New Mathematical Diversions. Washington, D.C.: Mathematical Association of America.

Gardner, Martin. 1989. The art of M. C. Escher. In Mathematical Carnival. Washington, D. C.: Mathematical Association of America.

Hofstadter, Douglas R. 1979. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books.

Hollist, J. Taylor. 2000. M C. Escher's association with scientists. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, ed. See http://www.sckans.edu/~bridges/ .

Levine, Howard. 1994. The art of mathematics, the mathematics of art. Leonardo 27 (No. 1): 87-89.

Levy, Silvio. 1993. Automatic generation of hyperbolic tilings. In The Visual Mind: Art and Mathematics, Michele Emmer, ed. Cambridge, Mass.: MIT Press.

Maor, Eli. 1987. To Infinity and Beyond: A Cultural History of the Infinite. Boston: Birkhäuser.

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

Seckel, Al. 2000. The Art of Optical Illusions. London, England: Carlton Books.

Sims, John. 2001. TimeSculpture—Constructing social geometries. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Sarhangi, Reza, and Slavik Jablan, eds. Available at http://members.tripod.com/vismath4/sims/index.html .

Weeks, Jeffrey R. 1985. The Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds. New York: Marcel Dekker.


Douglas Dunham:
http://www.d.umn.edu/~ddunham/
http://members.tripod.com/vismath4/dunham1/index.html
M. C. Escher:
http://www.mcescher.com/ and http://www.worldofescher.com/
John Safer:
http://www.johnsafer.com/
John Sims:
http://members.tripod.com/vismath4/simse/index.html

Corrections and Clarifications

Flap copy, corrected first sentence of second paragraph:
Most of us have been led to believe that mathematics is left-brain work, art is right-brain work, case closed.
p. 30, caption:
It is no longer true that "this is an unsolved problem."
p. 122, corrected caption:
A Penrose tiling pattern (right) offers an intriguing alternative to traditional, periodic patterns based on rhombs that create an illusion of an array of cubes (above).
p. 128, corrected quote (originally missing "the" before "time"):
"You can say the history of art is the history of different spaces, and these spaces are an embodiment of the mathematics of the time, of the geometry of the time."
p. 139:
The date when Johann Benedict Listing published his discovery should be 1861 instead of 1856.
p. 142, clarification:
Topologists generally apply the term "Möbius band" to not only the standard form (one half-twist) but also the symmetric version (three half-twists) and anything else "homeomorphic" to the standard form. For historical and cultural reasons, I apply the term only to the "standard" embedding of the Möbius band in three-dimensional space to distinguish this particular form from other embeddings.
p. 160, corrected first sentence of fourth paragraph:
Until the 1980s, mathematicians knew of only two other unbounded minimal surfaces of finite topology that don't curl around to intersect themselves.
p. 200:
Brent Collins' grandmother lived to the age of 102.
p. 226, corrected credit:
Credit for the photo on page 159 should go to Stan Wagon.

Additional Artists and Resources

Mel Bochner:
http://www.parasolpress.com/bochner.htm
http://www.akiraikedagallery.com/pe_bochner_nagoya.htm
http://www.arionpress.com/catalog/034.htm
Charles Demuth:
http://www.artcyclopedia.com/artists/demuth_charles.html
Agnes Denes:
http://asci.org/artsci99/denes.html
Jan Dibbets:
http://www.newyorkartworld.com/reviews/dibbets.html
Susan Happersett:
http://www.purgatorypiepress.com/artistsbooks_files/boxofgrowth.htm
http://www.sciencenews.org/20010609/mathtrek.asp
Clement Meadmore:
http://www.yaddo.org/Yaddo/OnsiteMeadmore.shtml
http://www.qc-art.com/html/meadmore.html
http://www.pyramidhill.org/main/1999Aug31220527.shtml
George Rickey:
http://www.davidsongallery.com/rickey.html
http://www.decordova.org/decordova/sculp_park/rickey.html
http://www.nga.gov/feature/sculptgarden/sculpt13.htm
http://www.stormking.org/GeorgeRickey.html
Irene Rousseau:
http://www.aboutmosaics.com/
John Sharp (sliceforms):
http://www.mathsyear2000.org/resources/slice/
Frank Stella:
http://www.artcyclopedia.com/artists/stella_frank.html
http://sheldon.unl.edu/HTML/ARTIST/Stella_F/PC.html
http://www.wired.com/wired/archive/7.03/stella.html
Dick Termes:
http://world.std.com/~brd/termes.html
http://www.westdakota.com/termes/default.htm
Roman Verostko:
http://www.verostko.com/
Elizabeth Whiteley:
http://www.koanart.com/beth.html
http://libweb.sonoma.edu/special/waa/whiteley/