References

This is not meant to be a complete reference to all books and/or articles relating to Escher, but a survey of some books, articles and website that may be useful to the reader.

Escher Related Books

We have used Visions of Symmetry and The Magic of M. C. Escher as textbooks for our course. We use Visions of Symmetry at the beginning of the course and we turn to The Magic of M. C. Escher later in the semester.

• Escher on Escher: Exploring the Infinite (Paperback) by M. C. Escher, J. W. Vermeulen, Karin Ford (Translator)

Publisher: Harry N. Abrams (1989); ISBN-10: 0810924145; ISBN-13: 978-0810924147

• M.C. Escher: Life and Complete Graphic Work by J L Locher.

Publisher: Harry N. Abrams (1992); ISBN-10: 0810981130;ISBN-13: 978-0810981133

• M.C. Escher : 29 Master prints (Paperback)by M. C. Escher

Publisher: Harry N. Abrams (1983);ISBN-10: 0810922681;ISBN-13: 978-0810922686

• The Magic of M. C. Escher by J. L. Locker

Publisher: Harry N. Abrams (2000); ISBN-10: 0810967200; ISBN-13: 978-0810967205

• The Magic Mirror of M.C. Escher (Taschen 25th Anniversary Series) by Bruno Ernst (Author), M. C. Escher

Publisher: Taschen; Taschen 25th Anniversary Ed edition (2007); ISBN-10: 3822837032; ISBN-13: 978-3822837030

• Visions of Symmetry - Notebooks, Periodic Drawings, and Related Work of M. C. Escher by Doris Schattschneider

Publisher: Harry N. Abrams; 2 edition (2004);ISBN-10: 0810943085; ISBN-13: 978-0810943087

Relevant Books

• Adventures With Impossible Figures (Paperback)by Bruno Ernst.

Publisher: Tarquin (1987); ISBN-10: 0906212545; ISBN-13: 978-0906212547

• Impossible Worlds: Adventures With Impossible Objects / Optical Illusions (Evergreen Series) (Paperback)by Bruno Ernst.

Publisher: Evergreen;(2006); ISBN-10: 3822854107; ISBN-13: 978-3822854105

• Tilings and Patterns by B. Grunbaum & G.C. Shepard, W.H. Freeman and Company, New York, 1986, 700 pages.

Articles

With thanks to Doris Schattschneider for most of these.

• Coxeter, H.S.M. "Crystal Symmetry and Its Generalizations", in "A Symposium on Symmetry.The Transactions of te Royal Society of Canada LI: Series III: Section Three (June 1957): 1-13.

• Coxeter, H.S.M. "The non-Eucliden Symmetry of Escher's Picture 'Circle Limit III'." Leonardo 12 (1979): 19-25, 32

• Coxeter, H.S.M. "The Trigonometry of Escher's Woodcut 'Circle Limit III' " Mathematical Intelligencer, Vol. 18, No. 4, pp 42-46. A reprint was made available by the AMS PDF file See also AMS page with links to images.

• Coxeter, H.S.M. "Angels and Devils." In The Mathematical Gardener, ed. David A. Klarner, 197-209 & Plate IV. Boston: Prindle, Weberr & Schmidt, 1981. Reprinted as Mathematical recreations: A Collection in Honor of Martin Gardner, Mineloa, NY: Dover, 1998

• Davis, Dan, "On a tiling scheme from M.C. Escher," Electronic Journal of Combinatorics, vol. 4 no.2 (1997) [Article in PostScript format]

• Dunham, Douglas, "Creating Repeating Hyperbolic Patterns—Old and New", In Artful Mathematics: The Heritage of M. C. Escher in AMS Notices 2003. PDF file from the AMS notices

• Gardner, Martin. "The Eerie Mathematical Art of Maurits C. Escher," Scientific American 214 (April 1966): 110-121. In Mathematical Carnival. Washington D.C.: Mathematical Association of America, 1989

• Gethner, Ellen, "On a generalization of a combinatorial problem posed by M.C. Escher," Proceedings of the Thirty-second Southeastern International Conference on Combinatorics, Graph Thory and Computing, v.153, 2001, pp 77-96

• Grunbaum, Branko "Levels of orderliness: global and local symmetry." In Symmetry 2000, eds. I. Hargittai and T.C. Laurent, pp 51-61. London: Portland Press, 2002.

• Mabry, R., Wagon, S. and Schattschneider, D, "Automating Escher's Combinatorial Patterns." Mathematica in Education and Research, vol 5, n0 4 (1996) 38-52

• Maor, Eli. "Maurits C. Escher - Master of the Infinite." In To Infinity and Beyond, pp 164-178. Boston: Birkhauser, 1987

• Polya, G. "Uber die Analogie der Kristallsymmetrie in der Ebene" Zeitschrift fur Kristallographie 60 (1924)

• Schattschneider, Doris. "The Polya-Escher Conection" 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

• Schattschneider, Doris. "Escher's Combinatorial Patterns" The Electronic Journal of Combinatorics, 4 (no 2) (1997) [Download PFD Version of Article ]

• Schattschneider, Doris and Dolbilin, N.. "One Corona is Enough for the Euclidean Plane." in Quasicrystals and Discrete Geometry, J. Patera ed., AMS, 1998, pp 193-199 and pp 207-246

• Schattschneider, Doris. "The Many Faces of Symmetry in the Works of M.C. Escher." In Symmetry 20000, I. Hargittai and T.C. Laurent, eds., pp 173-184. London: Portland Press, 2002.

• 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

Related Web Sites

Escher Related Sites:

• [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.

• [M.C.Escher Mindscapes] Page dedicated to Escher from the National Gallery of Canada.

• [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 "Symmatry and Tessellations" (Aimed at Middle School)

Geometry Related Sites:

• [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:

• [Tilings and Tessellations from ScienceU] This site has basic tiling information, the 17 wallpaper groups (animated!) and aperiodic & Penrose tilings.

• ["Complement Tiling"] From The Wolfram Demonstrations Project

• ["Wallpaper Groups."] by Weisstein, Eric W. From MathWorld--A Wolfram Web Resource.

Assorted Topics:

• [Fractal Geometry from Yale University ] An online course from Yale University. Full of great stuff, especially the Panorama of Fractals and Their Uses.

• [Jackson's Fractals] An article explaining the fratal nature of Jackson Pollock's art. Includes an explanation of fractal dimension.

• [Math Awareness Month - Mathematics and Art (2003)] This website features an Escher-inspired hyperbolic tessellation, essays by artists and mathematicians, and other resources. See for instance:
  • Hyperbolic Art and the Poster Pattern by Douglas Dunham
  • Mathematics and Art -- So Many Connections by Doris Schattschneider

• ["Penrose Stairway."] by Weisstein, Eric W. From MathWorld--A Wolfram Web Resource.