# 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 many of these.

**Symmetry and Tessellations:**

- 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. "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]*

- Maor, Eli. "Tiling the Plane." In
*To Infinity and Beyond*, pp 102-107. Boston: Birkhauser, 1987

- Maor, Eli. "Horror Vacui, Amor Infinity." In
*To Infinity and Beyond*, pp 155-163. Boston: Birkhauser, 1987 (Symmetry Groups)

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

- Schattschneider, Doris. "The Many Faces of Symmetry in the Works of M.C. Escher." In
*Symmetry 2000*, I. Hargittai and T.C. Laurent, eds., pp 173-184. London: Portland Press, 2002.

**Non-Euclidean Geometry:**

- 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.

- 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

- Peterson, Ivars,
*Fragments.*In*Fragments of Infinity: A Kaleidoscope of Math and Art*pp 207-218 John Wiley & Sons, Inc 2001.

**Mathematics and Art:**

- 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

- 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.

- Mankiewicz, Richard. "The Renaissance Perspective." In
*The Story of Mathematics*, pp 59-66. Princeton University Press, 2000

- Mankiewicz, Richard. "New Geometries." In
*The Story of Mathematics*, pp 125-132. Princeton University Press, 2000

- Mankiewicz, Richard. "Catching Infinity." (fractals) In
*The Story of Mathematics*, pp 147-152. Princeton University Press, 2000

- Mankiewicz, Richard. "Maths and Modern Art." In
*The Story of Mathematics*, pp 165-172. Princeton University Press, 2000

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

**The Fourth Dimension**

- Abbott, Edwin A.
*Flatland: A Romance of Many Dimensions (1880), Dover Thrift Edition.*

ISBN-10: 048627263X ; ISBN-13: 978-0486272634

Online Version: Flatland

Online Version with copies of the illustrations: Flatland

- Heinlein, Robert A.
*And he built a crooked house ...*[1]

- Peterson, Ivars,
*A Place in Space.*In*Fragments of Infinity: A Kaleidoscope of Math and Art*pp 35-60 John Wiley & Sons, Inc 2001.

**Other:**

- 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

- 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. Discussion of Fractals in "Some Functions and their Graphs." In
*To Infinity and Beyond*, pp 76-82. Boston: Birkhauser, 1987

- Maor, Eli. "The Mobius Strip." In
*To Infinity and Beyond*, pp 139-148. Boston: Birkhauser, 1987

- 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

- 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

- 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 "Symmetry 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:

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