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Reference
Donald W. Crowe: Symmetries of Culture. In: Bridges 2001. Pages 1–20
DOI
Abstract
Plane patterns, both one-color and two-color, can be naturally classified according to the symmetries they admit. In this survey the symmetries of the plane, and the resulting classification of patterns, are described. Following the lead of A. Speiser and E. Mueller the author studied patterns in various African contexts, and in the American Southwest, culminating in the book Symmetries of Culture with Dorothy Washburn. The results of field trips to Fiji and Tonga, applying the techniques from that book, are described and illustrated.
Extended Abstract
Bibtex
Used References
[1] G. W. Brainerd, Symmetry in primitive conventional design, American Antiquity 8(2),164-66,1942.
[2] D. W. Crowe, The geometry of African art. Part 1. Bakuba art, Journal of Geometry 1,169-182,1971.
[3] D.W. Crowe, The geometry of African art. Part 2. A catalog of Benin patterns, Historia Mathematica 2, 253-271, 1975.
[4] D.W. Crowe, The geometry of African art. Part 3. The smoking pipes of Begho, in The Geometric_Vein: The Coxeter Festschrift, edited by C. Davis, B. GrUnbaum, and F. A. Sherk, 177-189, New York: Springer, 1982.
[5] D.W. Crowe, The mosaic patterns of H. J Woods, in Symmetry: Unifying Human Understanding, edited by 1. Hargittai, 407-411, New York:, Pergamon, 1986.
[6] D.W. Crowe, Tongan symmetries, in Science of Pacific Island Peoples, Part IV, Education, LangUage, Patterns and Policy, edited by J. Morrison, P. Geraghty, and L. Crowl, Suva:Institute of Pacific Studies, 1994.
[7] D. W. Crowe and D. K. Washburn, Groups and geometry in the ceramic art of San Ildefonso, Algebras, Groups and Geometries 3(2), 263-277, 1985.
[8] D. W. Crowe and D. Nagy, Cakaudrove-style masi kesa of Fiji, Ars Textrina 18, 119-155, 1992.
[9] D. W. Crowe and R. Torrence, Admiralty Islands spear decorations: A minicatalog ofpmm patterns, Symmetry: Culture and Science 4(4), 385-396, 1993.
[10] R. Ewins, Symmetry and semiotics: The case of Fijjian bark-cloth decoration, to appear in Embedded Symmetries, Proceedings of a symposium at the Amerind Foundation, Dragoon, Arizona, April 13-17, 2000, edited by D. K. Washburn, University of New Mexico Press.
[11] E. Mueller, Gruppentheoretische und Strukturanalytische Untersuchungen der Maurischen Ornamente aus der Alhambra in Granada, Ph.D. diss., University of ZUrich, Riischlikon, 1944.
[12] A. O. Shepard, The Symmetry of Abstract Design with Special Reference to Ceramic Decoration, Contribution no. 47, Carnegie Institution of Washington Publications no. 574, 1948.
[13 ] A. Speiser, Die Theorie der Gruppen endlicher Ordnung, 2 nd edition, Berlin: Springer, 1927.
[14] D. K. Washburn and D. W. Crowe, Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, Seattle: University of Washington Press, 1988.
[15] C. Zaslavsky, Africa Counts: Number and Pattern in African Culture, Boston: Prindle, Weber & Schmidt, 1973.
Links
Full Text
http://archive.bridgesmathart.org/2001/bridges2001-1.pdf
