Lessons in Duality and Symmetry from M.C. Escher
Inhaltsverzeichnis
Reference
Doris Schattschneider: Lessons in Duality and Symmetry from M.C. Escher. In: Bridges 2008. Pages 1–8
DOI
Abstract
The Dutch graphic artist M.C. Escher (1898-1972) carried out mathematical investigations that led to symmetry drawings of three distinct kinds of tilings with two colors, capturing the essence of duality. He used several of these drawings as key elements in his prints that further expressed ideas of duality. One of the most complex of his “duality” tilings was realized in Delft ceramic tile, wrapped around a large column for a school in Baarn, Holland. Recently, a Salish artist in Victoria, BC, Canada, has independently produced a tiling that contains many of the same elements as Escher’s complex duality tilings.
Extended Abstract
Bibtex
Used References
[1] F.H. Bool, J.R. Kist, J.L. Locher, and F. Wierda, eds. M.C. Escher: His Life and Complete Graphic Work . New York: Harry N. Abrams, l982; Abradale Press, 1992.
[2] H.S.M. Coxeter, Coloured Symmetry. In M.C. Escher: Art and Science, H.S.M. Coxeter, M. Emmer, R. Penrose, and M.L. Teuber, editors, pp. 15–33. Amsterdam: North-Holland, 1986.
[3] A.W.M. Dress, The 37 combinatorial types of “Heaven and Hell” patterns in the Euclidean Plane. In Coxeter et al, (see [2]) pp. 35–45.
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[5] G. Pólya, Über die Analogie der Kristallsymmetrie in der Ebene. Zeitschrift für Kristallographie 60 (1924): 278-282.
[6] Scientific American, v. 204, no. 4, April 1961, cover and p. 4.
[7] D. Schattschneider, In Black and White: How to Create Perfectly Colored Symmetric Patterns. Computers and Mathematics With Applications 12B (1986): 673-695.
[8] D. Schattschneider, The Many Faces of Symmetry in the Work of M.C. Escher. In Symmetry 2000, ed. I. Hargittai and T.C. Laurent, 173-184. London: Portland Press, 2002.
[9] D. Schattschneider, M.C. Escher: Visions of Symmetry. New York: Harry Abrams, 2004.
[10] D.K. Washburn, and D.W. Crowe. Symmetries of Culture: Theory and Practice of Plane Pattern Analysis. Seattle: University of Washington Press, l988.
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Full Text
http://archive.bridgesmathart.org/2008/bridges2008-1.pdf
