Difference between revisions of "References"

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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.
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==Escher and His Work==
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*{{cite book | title=M.C. Escher: His Life and Complete Graphic Work | first=F.H. | last=Bool |coauthors=J.R.Kist, J.L. Locher, F. Wierda|others=Essays by B. Ernst, M.C. Escher|editor=J.L.Locher|publisher=Harry N. Abrams | year=1982 | isbn=0810981130}}<br>Escher's life history, and the complete catalog of all of his work.
  
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*{{cite book| title=The Magic Mirror of M.C. Escher| first=Bruno|last=Ernst|coauthors=M. C. Escher|publisher=Taschen|edition=Taschen 25th Anniversary|year=2007|origyear=1978|isbn=3822837032}}<br>Fifteen chapters, each detailing a theme in Escher's work.
  
==Escher Related Books==
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*{{cite book|title=M.C. Escher: The Graphic Work|first=M.C.|last=Escher|publisher=Taschen|year=2001|origyear=1959|isbn=3822858641}}<br>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, <cite>Grafiek en Tekeningen</cite>.
  
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.
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*{{cite book | title=M.C. Escher : 29 Master prints| first=M.C. |last=Escher| publisher=Harry N. Abrams|year=1983|isbn=0810922681}}.<br>Reproductions of 29 Escher prints, and nothing more.
  
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*{{cite book | last=Escher | first=M.C. | coauthors= J. W. Vermeulen|others=Karin Ford (Translator)|
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| title=Escher on Escher: Exploring the Infinite
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| publisher= Harry N. Abrams
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| year=1989
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| isbn=0810924145
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}}<br>A handful of letters, news clippings by or about Escher, and one longer two part lecture.  Some illustrations.
  
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*{{cite book|title=Gödel, Escher, Bach: an Eternal Golden Braid|first=Douglas|last=Hofstadter|year=1980|publisher=Basic Books|isbn=0465026567}}<br>A metaphorical fugue on minds and machines in the spirit of Lewis Carroll.
  
* ''Escher on Escher: Exploring the Infinite'' (Paperback) by M. C. Escher, J. W. Vermeulen, Karin Ford (Translator)
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*{{cite book| title=The Magic of M. C. Escher| first=J.L|last=Locher|publisher=Harry N. Abrams|year=2000| isbn=0810967200}}<br>  Beautiful coffee table book with large color reproductions, fold outs, and some of Escher's sketches and studies.
  
Publisher: Harry N. Abrams (1989); ISBN-10: 0810924145; ISBN-13: 978-0810924147
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*{{cite book|title=Visions of Symmetry - Notebooks, Periodic Drawings, and Related Work of M. C. Escher|first=Doris|last=Schattschneider|publisher=Harry N. Abrams|edition=2nd|year=2004|origyear=1990|isbn=0810943085}}<br>Definitive guide to Escher's regular division of the plane.
  
* ''M.C. Escher: Life and Complete Graphic Work'' by J L Locher.
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* Schattschneider, Doris. "The Polya-Escher Connection" ''Mathematics Magazine'' 60 (1987): 293-198
  
Publisher: Harry N. Abrams (1992); ISBN-10: 0810981130;ISBN-13: 978-0810981133
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* Schattschneider, Doris. "Escher's Metaphors" ''Scientific American'' 271 (Nov. 1994): 66-71
  
* ''M.C. Escher : 29 Master prints'' (Paperback)by M. C. Escher
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* Schattschneider, Doris. "Escher: A mathematician in spite of himself," ''Structural Topology'' 15 (1989); reprinted in ''The Lighter Side of Mathematics,'', MAA, 1994
 
 
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
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* {{cite journal|last=Schattschneider|first=Doris|title=The Mathematical Side of M.C. Escher|journal=AMS Notices|volume=57|number=6|year=2010|pages=706-718|url=http://www.ams.org/notices/201006/rtx100600706p.pdf}}
  
* ''Impossible Worlds: Adventures With Impossible Objects / Optical Illusions'' (Evergreen Series) (Paperback)by Bruno Ernst.
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*{{cite journal|last=Gardner|first=Martin|title=The Eerie Mathematical Art of Maurits C. Escher|journal=Scientific American|number=214|year=April 1966|pages=110-121}} Reprinted in ''Mathematical Carnival.'' Washington D.C.: Mathematical Association of America, 1989
  
Publisher: Evergreen;(2006); ISBN-10: 3822854107; ISBN-13: 978-3822854105
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==Symmetry and Tessellations==
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* {{cite book|title=Tilings and Patterns|first=Branko|last=Grünbaum|coauthors=G.C. Shepard|publisher=W.H. Freeman and Company|year=1986|isbn=0716711931}}<br>The definitive mathematical text on tessellations, crammed with beautiful black and white illustrations.
  
* ''Tilings and Patterns by B. Grunbaum & G.C. Shepard'', W.H. Freeman and Company, New York, 1986, 700 pages.
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* {{cite book|first=Dorothy K.|last=Washburn|coauthors=Donald W. Crowe|title=Symmetries of Culture:  Theory and Practice of Plane Pattern Analysis|year=1988|publisher=University of Washington Press|isbn=0295970847}}<br>  Classification of symmetry groups, with examples from world cultures.  The original source of the wallpaper group flowchart.
  
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* {{cite book|first=Dorothy K.|last=Washburn|coauthors=Donald W. Crowe|title=Symmetry Comes of Age: The Role of Pattern in Culture|year=2004|publisher=University of Washington Press|isbn=0295983663}}<br> A collection of articles by various authors.
  
==Articles==
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* {{cite book|last=Stevens|first=Peter S.|title=Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions|isbn=0262690888|publisher=The MIT Press|year=1981}}<br>Large collection of patterns from various sources, organized by symmetry group.
  
With thanks to Doris Schattschneider for many of these.
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* {{cite book|title=Symmetry|first=Hermann|last=Weyl|publisher=Princeton University Press|year=1952|isbn=0691080453}}<br>Two lyrical lectures on symmetry in art and science, followed by two much more technical lectures on symmetry groups.
  
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* {{cite journal|last=Pólya|first=George|title=Uber die Analogie der Kristallsymmetrie in der Ebene|journal=Zeitschrift fur Kristallographie|number=60|year=1924}}  The original source for the classification of the 17 wallpaper symmetry gropus, including an illustration that inspired Escher.
  
'''Symmetry and Tessellations:'''
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* {{cite journal|last=Coxeter|first=H.S.M|title=Crystal Symmetry and Its Generalizations|journal=The Transactions of the Royal Society of Canada|series=III|volume=51|month=June|year=1957|pages=1-13}}
  
* 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.
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* {{cite journal|last=Coxeter|first=H.S.M.|title=Angels and Devils|journal=The Mathematical Gardener|editor=David A. Klarner|pages=197-209 & Plate IV|publisher=Prindle, Weberr & Schmidt|year=1981}} Reprinted as ''Mathematical recreations: A Collection in Honor of Martin Gardner'', Mineola, NY: Dover, 1998
  
* 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
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* {{cite journal|last=Davis|first=Dan|title=On a tiling scheme from M.C. Escher|journal=Electronic Journal of Combinatorics|volume=4|number=2|year=1997}} [http://www.combinatorics.org/Volume_4/PostScriptfiles/v4i2r23.ps Article in PostScript format]
  
* Davis, Dan, "On a tiling scheme from M.C. Escher," ''Electronic Journal of Combinatorics, vol. 4 no.2 (1997) [[http://www.combinatorics.org/Volume_4/PostScriptfiles/v4i2r23.ps Article in PostScript format]]
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* {{cite journal|last=Schattschneider|first=Doris|title=The Many Faces of Symmetry in the Works of M.C. Escher|journal=Symmetry 2000|editor=I. Hargittai and T.C. Laurent|pages=173-184|publisher=London: Portland Press|year=2002}}
  
* Maor, Eli. "Tiling the Plane." In ''To Infinity and Beyond'', pp 102-107. Boston: Birkhauser, 1987
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* {{cite journal|last=Grünbaum|first=Branko|title=Levels of orderliness: global and local symmetry|journal=Symmetry 2000|editor=I. Hargittai and T.C. Laurent|pages=51-61|publisher=London: Portland Press|year=2002}}
  
* Maor, Eli. "Horror Vacui, Amor Infinity." In ''To Infinity and Beyond'', pp 155-163. Boston: Birkhauser, 1987 (Symmetry Groups)
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* {{cite journal|last=Schattschneider|first=Doris|title=Escher's Combinatorial Patterns|journal=The Electronic Journal of Combinatorics|volume=4|number=2|year=1997}} [http://www.combinatorics.org/Volume_4/PDF/v4i2r17.pdf  (online version)]<br>Escher's "potato stamp" game for making patterns with carved square blocks.
  
* Polya, G. "Uber die Analogie der Kristallsymmetrie in der Ebene" Zeitschrift fur Kristallographie'' 60 (1924)
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* {{cite journal|last=Grünbaum|first=Branko|title=What Symmetry Groups Are Present in the Alhambra?|journal=Notices of the AMS|volume=43|number=6|year=June/July 2006}} [https://digital.lib.washington.edu/dspace/bitstream/handle/1773/2349/Alhambra.Grunbaum.pdf (online version)]<br>A careful study of patterns at the Alhambra, intended to show that <em>not</em> all 17 groups are present.
  
* 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.
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* {{cite book|title=Geometric Concepts in Islamic Art|first=Isssam|last=El Said|coauthors=A. Parman|publisher=World of Islam Festival Publishing|year=1976|isbn=0905035038}}<br>A manual for constructing traditional Islmaic symmetry and interlace patterns.
  
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==Non-Euclidean Geometry==
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* {{cite book|last=Greenberg|first=Marvin|title=Euclidean and Non-Euclidean Geometries|edition=2nd| year=1980|isbn=0716711036|publisher=Freeman}}<br>Focus on history, axioms, and hyperbolic geometry.
  
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* {{cite book|last=Stillwell|first=John|title=The Four Pillars of Geometry|publisher=Springer|year=2005}}<br>Undergraduate text in mathematics treats projective geometry and perspective among other topics.
  
'''Non-Euclidean Geometry:'''
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* {{cite book|last=Singer|first=David A.|title=Geometry:Plane and Fancy|publisher=Springer|year=1998}}<br>Undergraduate text in mathematics treats Euclidean, spherical, and hyperbolic geometry along with tessellations of all three.
  
* Coxeter, H.S.M. "The non-Eucliden Symmetry of Escher's Picture 'Circle Limit III'." ''Leonardo'' 12 (1979): 19-25, 32
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===Circle Limits===
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* {{cite journal|last=Coxeter|first=H.S.M.|title=The Non-Euclidean Symmetry of Escher's Picture 'Circle Limit III'|journal=Leonardo|volume=12|year=1979|pages=19-25, 32}}.<br>Describes how Escher created the print.
  
* 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 [http://www.ams.org/featurecolumn/archive/circle_limit_iii.pdf PDF file]  See also [http://www.ams.org/featurecolumn/archive/circle_limit_iii.html AMS page with links to images.]
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* {{cite journal|last=Coxeter|first=H.S.M.|title=The Trigonometry of Escher's Woodcut 'Circle Limit III'|journal=Mathematical Intelligencer|volume=18|number=4|pages=42-46.}} A reprint was made available by the AMS [http://www.ams.org/featurecolumn/archive/circle_limit_iii.pdf PDF file]  See also [http://www.ams.org/featurecolumn/archive/circle_limit_iii.html 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. [http://www.ams.org/notices/200304/fea-escher.pdf PDF file from the AMS notices]
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* {{cite journal|last=Dunham|first=Douglas|title=Creating Repeating Hyperbolic Patterns—Old and New|journal=AMS Notices|year=2003|month=April|pages=452-455|url=http://www.ams.org/notices/200304/fea-escher.pdf}} Algorithms for drawing a hyperbolic tessellation.
  
* Peterson, Ivars, ''Fragments.'' In ''Fragments of Infinity: A Kaleidoscope of Math and Art''  pp 207-218  John Wiley & Sons, Inc 2001.
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*{{cite web|last=Casselman|first=Bill|title=How Did Escher Do It? (How did M. C. Escher draw his Circle Limit figures…)|url=http://www.ams.org/samplings/feature-column/fcarc-circle-limit|year=2010|month=June|publisher=AMS website Feature Column}}
  
'''Mathematics and Art:'''
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==Mathematics and Art==
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* {{cite book|last=Field|first=J.V.|title=Piero della Francesca.  A Mathematician's Art|publisher=Yale University Press|year=2005|isbn= 0300103425}}
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* {{cite book|title=Adventures With Impossible Figures|first=Bruno|last=Ernst|isbn=0906212545|year=1987|publisher=Tarquin}}
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* {{cite book|title=Impossible Worlds: Adventures With Impossible Objects/Optical Illusions|first=Bruno|last=Ernst|publisher=Taschen|year=2006|isbn=3822854107}}<br>Is this just a repackaging of two other Ernst books?
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* {{cite book|title=The Visual Mind: Art and Mathematics|first=Michele|last=Emmer|year=1993|isbn=026205048X}}<br>Thirty-six articles by mathematicians and artists on visualization, computer graphics, symmetry, and perspective.  Most reprinted from the journal Leonardo.
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* {{cite book|last=Peterson|first=Ivars|title=Fragments of Infinity: A Kaleidoscope of Math and Art|publisher= John Wiley & Sons, Inc.|year=2001|isbn= 0471165581|pages=207-218}}<br>A recreational math book with a shallow but broad coverage of artists working with mathematical ideas.
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* {{cite book|last=Molderings|first=Herbert|title=Duchamp and the Aestrhetics of Chance|publisher=Columbia University Press|year=2010|isbn=9780231147620}}
  
* 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
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==The Fourth Dimension==
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* {{cite book|last=Henderson|first=Linda D|title=The Fourth Dimension and Non-Euclidean Geometry in Modern Art|publisher=Princeton University Press|year=1993}}<br>The definitive source on the influence of 4D on the cubists and other artists of the period.
  
* 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.
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* {{cite book|last=Banchoff|first=Thomas|title=Beyond the Third Dimension|year=1990|publisher=Scientific American Library}}
  
* Mankiewicz, Richard. "The Renaissance Perspective." In ''The Story of Mathematics'', pp 59-66. Princeton University Press, 2000
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* {{cite book|last=Robbin|first=Tony|title=Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought|year=2006|publisher=Yale University Press|isbn=0300110391}}<br>Discusses the influence of 4D on cubists, especially Picasso, the projection model, and spacetime physics.
  
* Mankiewicz, Richard. "New Geometries." In ''The Story of Mathematics'', pp 125-132. Princeton University Press, 2000
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===Fiction===
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* {{cite book|last=Abbott|first=Edwin A.|title=Flatland: A Romance of Many Dimensions|year=1880|edition=Dover Thrift Edition|isbn=048627263X}} Freely available online, for example at http://www.alcyone.com/max/lit/flatland/ or see [[wikipedia:Flatland]] for a list.
  
* Mankiewicz, Richard. "Catching Infinity." (fractals) In ''The Story of Mathematics'', pp 147-152. Princeton University Press, 2000
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* {{cite journal|last=Heinlein|first=Robert A|title=''... And he built a crooked house ...''|year=1941|journal=Astounding Science Fiction}}<br>Short science fiction story, available online at http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html .
  
* Mankiewicz, Richard. "Maths and Modern Art." In ''The Story of Mathematics'', pp 165-172. Princeton University Press, 2000
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* {{cite book|last=L'Engle|first=Madeleine|title="A Wrinkle In Time"|year=1962}}
  
* Maor, Eli. "Maurits C. Escher - Master of the Infinite." In ''To Infinity and Beyond'', pp 164-178. Boston: Birkhauser, 1987
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==Recreational Math Books With Broad Coverage==
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* {{cite book|last=Mankiewicz|first=Richard|title=The Story of Mathematics|publisher=Princeton University Press|year=2000}}<br>This recreational math book has many relevant chapters, including "The Renaissance Perspective", "New Geometries", "Catching Infinity" (fractals), and "Maths and Modern Art."
  
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* {{cite book|last=Maor|first=Eli|title=To Infinity and Beyond|publisher=Birkhauser|year=1987}}<br>Recreational math book with sections "Maurits C. Escher - Master of the Infinite","Tiling the Plane", and more.
  
'''The Fourth Dimension'''
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==Other==
 
 
* Abbott, Edwin A. ''Flatland: A Romance of Many Dimensions (1880), Dover Thrift Edition.  ISBN-10: 048627263X ; ISBN-13: 978-0486272634
 
 
 
**Online Version: [http://www.alcyone.com/max/lit/flatland/ Flatland]
 
 
 
**Online Version with copies of the illustrations: [http://www.geom.uiuc.edu/~banchoff/Flatland/ Flatland]
 
 
 
*Heinlein, Robert A. ''And he built a crooked house ...'' [http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html ]
 
 
 
* 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) [[http://www.combinatorics.org/Volume_4/PDF/v4i2r17.pdf  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. [http://www.ams.org/notices/200304/fea-escher.pdf PDF file from the AMS notices]
 
* 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. [http://www.ams.org/notices/200304/fea-escher.pdf PDF file from the AMS notices]
  
==Related Web Sites ==
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==Web Sites ==
 
 
 
 
'''Escher Related Sites:'''
 
 
 
* [[http://www.mcescher.com/ 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.
 
 
 
* [[http://www.escherinhetpaleis.nl/ Escher in het Paleis]] Website of the museum in The Hague, the Netherlands, dedicated to M.C. Escher.
 
  
* [[http://cybermuse.gallery.ca/cybermuse/youth/escher/index_e.jsp M.C.Escher Mindscapes]] Page dedicated to Escher from the National Gallery of Canada.
 
  
* [[http://escherdroste.math.leidenuniv.nl/ 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.
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===Escher Related===
  
* [[http://britton.disted.camosun.bc.ca/jbescher.htm 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)
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* [http://www.mcescher.com/ 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.
  
 +
* [http://www.escherinhetpaleis.nl/ Escher in het Paleis] Website of the museum in The Hague, the Netherlands, dedicated to M.C. Escher.
  
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* [http://cybermuse.gallery.ca/cybermuse/youth/escher/index_e.jsp M.C.Escher Mindscapes] Page dedicated to Escher from the National Gallery of Canada.
  
'''Geometry Related Sites:'''
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* [http://escherdroste.math.leidenuniv.nl/ 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.
  
* [[http://www.geometrygames.org/ Jeff Weeks' Geometry Games ]] Jeff Weeks’ Topology and Geometry Software. This includes the torus and klein-bottle games, Kali, Kaleidotile and more.
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* [http://britton.disted.camosun.bc.ca/jbescher.htm 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)
  
* [[http://merganser.math.gvsu.edu/easel/  Spherical Easel]] Spherical Easel is a program for creating interactive diagrams in spherical geometry.
 
  
* [[http://www.cs.unm.edu/%7Ejoel/NonEuclid/NonEuclid.html  Non-Euclid]] A Java based program that allows one to explore hyperbolic geometry.
 
  
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===Geometry Related===
  
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* [http://www.geometrygames.org/ Jeff Weeks' Geometry Games ] Jeff Weeks’ Topology and Geometry Software. This includes the torus and klein-bottle games, Kali, Kaleidotile and more.
  
'''Tessellations:'''
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* [http://merganser.math.gvsu.edu/easel/  Spherical Easel] Spherical Easel is a program for creating interactive diagrams in spherical geometry.
  
* [[http://www.scienceu.com/geometry/articles/tiling/index.html Tilings and Tessellations from ScienceU]] This site has basic tiling information, the 17 wallpaper groups (animated!) and aperiodic & Penrose tilings.
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* [http://www.cs.unm.edu/%7Ejoel/NonEuclid/NonEuclid.html Non-Euclid] A Java based program that allows one to explore hyperbolic geometry.
  
*  [[http://demonstrations.wolfram.com/ComplementTiling/  "Complement Tiling"]] From The Wolfram Demonstrations Project
 
  
*  [[http://mathworld.wolfram.com/WallpaperGroups.html  "Wallpaper Groups."]]  by Weisstein, Eric W.  From MathWorld--A Wolfram Web Resource.
 
  
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===Tessellations===
  
 +
* [http://www.scienceu.com/geometry/articles/tiling/index.html Tilings and Tessellations from ScienceU] This site has basic tiling information, the 17 wallpaper groups (animated!) and aperiodic & Penrose tilings.
  
'''Assorted Topics:'''
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*  [http://demonstrations.wolfram.com/ComplementTiling/  "Complement Tiling"] From The Wolfram Demonstrations Project
  
* [[http://classes.yale.edu/Fractals/ Fractal Geometry from Yale University ]] An online course from Yale University. Full of great stuff, especially the Panorama of Fractals and Their Uses.
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* [http://mathworld.wolfram.com/WallpaperGroups.html  "Wallpaper Groups."] by Weisstein, Eric WFrom MathWorld--A Wolfram Web Resource.  
  
* [[http://plus.maths.org/issue9/news/pollock/ Jackson's Fractals]] An article explaining the fratal nature of Jackson Pollock's art. Includes an explanation of fractal dimension.
+
===Art Related===
 +
[[Mathematical Artists]]
  
* [[http://www.mathaware.org/mam/03/ 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:  
+
===Assorted Topics===
 +
* [http://www.mi.sanu.ac.yu/vismath/ VisMath].  The Art and Science Electronic Journal of ISIS-Symmetry.
 +
* [http://classes.yale.edu/Fractals/ Fractal Geometry]. An online course from Yale University. Full of great stuff, especially the  Panorama of Fractals and Their Uses.
 +
* [http://plus.maths.org/issue9/news/pollock/ Jackson's Fractals]. An article explaining the fratal nature of Jackson Pollock's art. Includes an explanation of fractal dimension.
 +
* [http://www.mathaware.org/mam/03/ 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:  
 
** [http://www.mathaware.org/mam/03/essay1.html Hyperbolic Art and the Poster Pattern by Douglas Dunham]  
 
** [http://www.mathaware.org/mam/03/essay1.html Hyperbolic Art and the Poster Pattern by Douglas Dunham]  
 
** [http://www.mathaware.org/mam/03/essay3.html Mathematics and Art -- So Many Connections by Doris Schattschneider]
 
** [http://www.mathaware.org/mam/03/essay3.html Mathematics and Art -- So Many Connections by Doris Schattschneider]
  
* [[http://mathworld.wolfram.com/PenroseStairway.html "Penrose Stairway."]] by Weisstein, Eric W.  From MathWorld--A Wolfram Web Resource.
+
* [http://mathworld.wolfram.com/PenroseStairway.html Penrose Stairway] by Weisstein, Eric W.  From MathWorld--A Wolfram Web Resource.
 +
* [http://www.math.dartmouth.edu/~matc/eBookshelf/index.html MATC Electronic Bookshelf].  Interdisciplinary materials including:
 +
** [http://math.dartmouth.edu/%7Ematc/math5.geometry/ Geometry in Art & Architecture] by Paul Calter.
 +
** [http://math.dartmouth.edu/~matc/math5.pattern/index.html Pattern] by Pippa Drew and Dorothy Wallace.

Latest revision as of 12:35, 21 November 2013

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 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