The Symmetry of “Circle Limit IV” and Related Patterns

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Reference

Douglas Dunham: The Symmetry of “Circle Limit IV” and Related Patterns. In: Bridges 2009. Pages 163–168

DOI

Abstract

M.C. Escher’s print Circle Limit IV is the last of his four “Circle Limit” patterns. There are two questions one can ask about the symmetry of Circle Limit IV. First, what is the correct orientation in which to display the print? Second, what is the symmetry group of the pattern? We answer those questions and show some new patterns related to Circle Limit IV.

Extended Abstract

Bibtex

Used References

[1] J. Conway, H. Burgiel, C. Goodman-Strauss The Symmetries of Things, A.K. Peters, Ltd., Wellesley, MA, 2008. ISBN 1-56881-220-5

[2] H.S.M. Coxeter and W.O.J. Moser, Generators and Relations for Discrete Groups Springer-Verlag, Berlin, 1972. ISBN: 3540058370

[3] M.C. Escher, M.C. Escher The Graphic Work, Barnes & Noble/TASCHEN, New York, 2007. ISBN 0-7607-9669-6

[4] Official Escher web site: http://www.mcescher.com/

[5] M. Greenberg, Euclidean & Non-Euclidean Geometry, Third Edition: Development and History, 3nd Ed., W. H. Freeman, Inc., New York, 1993. ISBN 0716724464

[6] M. Greenberg, Euclidean & Non-Euclidean Geometry: Development and History, 4th Ed., W. H. Free- man, Inc., New York, 2008. ISBN 0-7167-9948-0

[7] P. Henry-Labord`ere, Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing, Chapman & Hall/CRC Press, 2008. ISBN 1-4200-8699-5

[8] S. Kalajdzievski, Math and Art: an Introduction to Visual Mathematics, Chapman & Hall/CRC Press, 2008. ISBN 1584889136

[9] J.L. Locher (ed.), M.C. Escher, His Life and Complete Graphic Work (English edition), Harry N. Abrams, Inc., New York, 1982. ISBN 0-8100-0858-1

[10] D. Schattschneider, M.C. Escher: Visions of Symmetry, 2nd Ed., Harry N. Abrams, Inc., New York, 2004. ISBN 0-8109-4308-5

[11] J. Yen and C.H. S ́equin, Escher Sphere Construction Kit, Proceedings of the 2001 ACM Symposium on Interactive 3D Graphics, (2001) 95–98. http://portal.acm.org/citation.cfm?id=364371


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http://archive.bridgesmathart.org/2009/bridges2009-163.pdf

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http://archive.bridgesmathart.org/2009/bridges2009-163.html