References

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Escher and His Work

  • Bool, F.H.; J.R.Kist, J.L. Locher, F. Wierda (1982). in J.L.Locher: M.C. Escher: His Life and Complete Graphic Work, Essays by B. Ernst, M.C. Escher, Harry N. Abrams. ISBN 0810981130.
    Escher's life history, and the complete catalog of all of his work.
  • Ernst, Bruno; M. C. Escher [1978] (2007). The Magic Mirror of M.C. Escher, Taschen 25th Anniversary, Taschen. ISBN 3822837032.
    Fifteen chapters, each detailing a theme in Escher's work.
  • Escher, M.C. [1959] (2001). M.C. Escher: The Graphic Work. Taschen. ISBN 3822858641.
    A brief introduction by Escher, then 76 mediocre reproductions of Escher's artwork, along with brief discussions of each. Translated from the 1959 Dutch edition, Grafiek en Tekeningen.
  • Escher, M.C. (1983). M.C. Escher : 29 Master prints. Harry N. Abrams. ISBN 0810922681..
    Reproductions of 29 Escher prints, and nothing more.
  • Escher, M.C.; J. W. Vermeulen (1989). Escher on Escher: Exploring the Infinite, Karin Ford (Translator), Harry N. Abrams. ISBN 0810924145.
    A handful of letters, news clippings by or about Escher, and one longer two part lecture. Some illustrations.
  • Hofstadter, Douglas (1980). Gödel, Escher, Bach: an Eternal Golden Braid. Basic Books. ISBN 0465026567.
    A metaphorical fugue on minds and machines in the spirit of Lewis Carroll.
  • Locher, J.L (2000). The Magic of M. C. Escher. Harry N. Abrams. ISBN 0810967200.
    Beautiful coffee table book with large color reproductions, fold outs, and some of Escher's sketches and studies.
  • Schattschneider, Doris [1990] (2004). Visions of Symmetry - Notebooks, Periodic Drawings, and Related Work of M. C. Escher, 2nd, Harry N. Abrams. ISBN 0810943085.
    Definitive guide to Escher's regular division of the plane.
  • Schattschneider, Doris. "The Polya-Escher Connection" Mathematics Magazine 60 (1987): 293-198
  • Schattschneider, Doris. "Escher's Metaphors" Scientific American 271 (Nov. 1994): 66-71
  • Schattschneider, Doris. "Escher: A mathematician in spite of himself," Structural Topology 15 (1989); reprinted in The Lighter Side of Mathematics,, MAA, 1994
  • Gardner, Martin (April 1966). "The Eerie Mathematical Art of Maurits C. Escher". Scientific American: 110-121. Reprinted in Mathematical Carnival. Washington D.C.: Mathematical Association of America, 1989

Symmetry and Tessellations

  • Grünbaum, Branko; G.C. Shepard (1986). Tilings and Patterns. W.H. Freeman and Company. ISBN 0716711931.
    The definitive mathematical text on tessellations, crammed with beautiful black and white illustrations.
  • Washburn, Dorothy K.; Donald W. Crowe (1988). Symmetries of Culture: Theory and Practice of Plane Pattern Analysis. University of Washington Press. ISBN 0295970847.
    Classification of symmetry groups, with examples from world cultures. The original source of the wallpaper group flowchart.
  • Washburn, Dorothy K.; Donald W. Crowe (2004). Symmetry Comes of Age: The Role of Pattern in Culture. University of Washington Press. ISBN 0295983663.
    A collection of articles by various authors.
  • Stevens, Peter S. (1981). Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions. The MIT Press. ISBN 0262690888.
    Large collection of patterns from various sources, organized by symmetry group.
  • Weyl, Hermann (1952). Symmetry. Princeton University Press. ISBN 0691080453.
    Two lyrical lectures on symmetry in art and science, followed by two much more technical lectures on symmetry groups.
  • Pólya, George (1924). "Uber die Analogie der Kristallsymmetrie in der Ebene". Zeitschrift fur Kristallographie. The original source for the classification of the 17 wallpaper symmetry gropus, including an illustration that inspired Escher.
  • Coxeter, H.S.M (June 1957). "Crystal Symmetry and Its Generalizations". The Transactions of the Royal Society of Canada 51: 1-13.
  • Coxeter, H.S.M. (1981). "Angels and Devils". The Mathematical Gardener: 197-209 & Plate IV. Prindle, Weberr & Schmidt. Reprinted as Mathematical recreations: A Collection in Honor of Martin Gardner, Mineola, NY: Dover, 1998
  • Schattschneider, Doris (2002). "The Many Faces of Symmetry in the Works of M.C. Escher". Symmetry 2000: 173-184. London: Portland Press.
  • Grünbaum, Branko (2002). "Levels of orderliness: global and local symmetry". Symmetry 2000: 51-61. London: Portland Press.
  • Schattschneider, Doris (1997). "Escher's Combinatorial Patterns". The Electronic Journal of Combinatorics 4. (online version)
    Escher's "potato stamp" game for making patterns with carved square blocks.
  • Grünbaum, Branko (June/July 2006). "What Symmetry Groups Are Present in the Alhambra?". Notices of the AMS 43. (online version)
    A careful study of patterns at the Alhambra, intended to show that not all 17 groups are present.
  • El Said, Isssam; A. Parman (1976). Geometric Concepts in Islamic Art. World of Islam Festival Publishing. ISBN 0905035038.
    A manual for constructing traditional Islmaic symmetry and interlace patterns.

Non-Euclidean Geometry

  • Greenberg, Marvin (1980). Euclidean and Non-Euclidean Geometries, 2nd, Freeman. ISBN 0716711036.
    Focus on history, axioms, and hyperbolic geometry.
  • Stillwell, John (2005). The Four Pillars of Geometry. Springer.
    Undergraduate text in mathematics treats projective geometry and perspective among other topics.
  • Singer, David A. (1998). Geometry:Plane and Fancy. Springer.
    Undergraduate text in mathematics treats Euclidean, spherical, and hyperbolic geometry along with tessellations of all three.

Circle Limits

  • Coxeter, H.S.M. (1979). "The Non-Euclidean Symmetry of Escher's Picture 'Circle Limit III'". Leonardo 12: 19-25, 32..
    Describes how Escher created the print.
  • Coxeter, H.S.M.. "The Trigonometry of Escher's Woodcut 'Circle Limit III'". Mathematical Intelligencer 18: 42-46.. A reprint was made available by the AMS PDF file See also AMS page with links to images.

Mathematics and Art

  • Field, J.V. (2005). Piero della Francesca. A Mathematician's Art. Yale University Press. ISBN 0300103425.
  • Ernst, Bruno (1987). Adventures With Impossible Figures. Tarquin. ISBN 0906212545.
  • Ernst, Bruno (2006). Impossible Worlds: Adventures With Impossible Objects/Optical Illusions. Taschen. ISBN 3822854107.
    Is this just a repackaging of two other Ernst books?
  • Emmer, Michele (1993). The Visual Mind: Art and Mathematics. ISBN 026205048X.
    Thirty-six articles by mathematicians and artists on visualization, computer graphics, symmetry, and perspective. Most reprinted from the journal Leonardo.
  • Peterson, Ivars (2001). Fragments of Infinity: A Kaleidoscope of Math and Art. John Wiley & Sons, Inc., 207-218. ISBN 0471165581.
    A recreational math book with a shallow but broad coverage of artists working with mathematical ideas.
  • Molderings, Herbert (2010). Duchamp and the Aestrhetics of Chance. Columbia University Press. ISBN 9780231147620.

The Fourth Dimension

  • Henderson, Linda D (1993). The Fourth Dimension and Non-Euclidean Geometry in Modern Art. Princeton University Press.
    The definitive source on the influence of 4D on the cubists and other artists of the period.
  • Banchoff, Thomas (1990). Beyond the Third Dimension. Scientific American Library.
  • Robbin, Tony (2006). Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought. Yale University Press. ISBN 0300110391.
    Discusses the influence of 4D on cubists, especially Picasso, the projection model, and spacetime physics.

Fiction

  • L'Engle, Madeleine (1962). "A Wrinkle In Time".

Recreational Math Books With Broad Coverage

  • Mankiewicz, Richard (2000). The Story of Mathematics. Princeton University Press.
    This recreational math book has many relevant chapters, including "The Renaissance Perspective", "New Geometries", "Catching Infinity" (fractals), and "Maths and Modern Art."
  • Maor, Eli (1987). To Infinity and Beyond. Birkhauser.
    Recreational math book with sections "Maurits C. Escher - Master of the Infinite","Tiling the Plane", and more.

Other

  • Smit, B. de, Lenstra Jr, H.W., "The Mathematical Structure of Escher's Print Gallery" In Artful Mathematics: The Heritage of M. C. Escher in AMS Notices 2003. PDF file from the AMS notices

Web Sites

Escher Related

  • The Official Escher website On this website you can find information about the use of M.C. Escher's work, a short biography, news, bibliography, links and some fun stuff like a Virtual Ride through some of his works.
  • Escher in het Paleis Website of the museum in The Hague, the Netherlands, dedicated to M.C. Escher.
  • Escher and the Droste effect Website from Leiden University in the Netherlands. The website aims to visualize the mathematical structure behind Escher's Print Gallery. In this print there is a blank space in the middle and several methods are shown for completing the picture.
  • Escher in the Classroom Website by Jill Britton. Great resoource for symmetry and tessellations. Materials accompany her book "Symmetry and Tessellations" (Aimed at Middle School)


Geometry Related

  • Jeff Weeks' Geometry Games Jeff Weeks’ Topology and Geometry Software. This includes the torus and klein-bottle games, Kali, Kaleidotile and more.
  • Spherical Easel Spherical Easel is a program for creating interactive diagrams in spherical geometry.
  • Non-Euclid A Java based program that allows one to explore hyperbolic geometry.


Tessellations

Art Related

Mathematical Artists

Assorted Topics