Hyperbolic Islamic Patterns -- A Beginning
Inhaltsverzeichnis
Reference
Douglas Dunham: Hyperbolic Islamic Patterns -- A Beginning. In: Bridges 2001. Pages 247–254
DOI
Abstract
For more than a millennium, Islamic artists and craftsmen have used geometric patterns to decorate buildings, cloth, pottery, and other artifacts. Many of these patterns were "wallpaper" patterns - they were planar patterns that repeated in two different directions. Recently related patterns have also been drawn on the Platonic solids, which can conceptually be projected outward onto their circumscribing spheres, thus utilizing a second of the three "classical geometries". We extend this process by exhibiting repeating Islamic patterns in hyperbolic geometry, the third classical geometry.
Extended Abstract
Bibtex
Used References
[1] Syed Jan Abas and Amer Shaker Salman, Geometric and Group~Theoretic Methods for Computer Graphic Studies of Islamic Symmetric Patterns, Computer Graphics Forum, Vol. 11 pp. 43-53, 1992.
[2] Syed Jan Abas and Amer Shaker Salman, Symmetries of Islamic Geometrical Patterns, World Scientific Publishing Co., New Jersey, 1995.
[3] 1. Bourgoin, Arabic Geometrical Pattern & Design, Dover Publications, Inc., New York, 1973.
[4] H. S. M. Coxeter and W. O. J. Moser, Generators and Relationsfor Discrete Groups, 4th Ed., Springer- Verlag, New York, 1980.
[5] B. Griinnbaum and G. C. Shephard, Interlace Patterns in Islamic and Moorish Art, Leonardo, Vol. 25, No. 3/4,pp. 331-339,1992.
[6] Owen Jones, The Grammar of Ornament, Dover Publications, Inc., New York, 1989.
[7] Craig S. Kaplan, Computer Generated Islamic Star Patterns, Bridges 2000 Conference Proceedings, pp. 105-112,2000.
[8] A. J. Lee, Islamic Star Patte~s, Muqarnas, Vol. 4, pp. 182-197, 1995.
[9] D. Schattschneider, Visions ofSymmetry: Notebooks, Periodic Drawings, andRelatedWorkofM. C. Es- cherW. H. Freeman, New York, 1990.
[10] Eva Wilson, Islamic Designsfor Artists and Craftspeople, Dover Publications, Inc., New York, 1988.
Links
Full Text
http://archive.bridgesmathart.org/2001/bridges2001-247.pdf