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Reference
Tiffany C. Inglis and Craig S. Kaplan: Circle patterns in Gothic Architecture. In: Bridges 2012. Pages 133–140
DOI
Abstract
Inspired by Gothic-influenced architectural styles, we analyze some of the circle patterns found in rose windows and semi-circular arches. We introduce a recursive circular ring structure that can be represented using a set-like notation, and determine which structures satisfy a set of tangency requirements. To fill in the gaps between tangent circles, we add Appollonian circles to each triplet of pairwise tangent circles. These ring structures provide the underlying structure for many designs, including rose windows, Celtic knots and spirals, and Islamic star patterns.
Extended Abstract
Bibtex
Used References
[1] Benno Artmann. The cloisters of Hauterive. In Kim Williams, editor, Nexus: Architecture and Mathematics, pages 15–25, June 1996.
[2] George Bain. The Methods of Constructions of Celtic Art. Dover Publications, Inc., New York, 1973.
[3] Jean Bony. French Gothic Architecture of the 12th and 13th Centuries. University of California Press, 1985.
[4] Archibald H. Christie. Traditional methods of pattern designing; an introduction to the study of the decorative art. Oxford: Clarendon press, 1910.
[5] Sir Banister Fletcher. Sir Banister Fletcher’s A History of Architecture. Architectural Press, 20th edition, 1996.
[6] Craig S. Kaplan. Islamic star patterns from polygons in contact. In GI ’05: Proceedings of the 2005 conference on Graphics Interface, 2005.
[7] David Mumford, Caroline Series, and David Wright. Indra’s Pearls: The Vision of Felix Klein. Cambridge University Press, Cambridge, 2002.
[8] Kenneth Stephenson. Introduction to Circle Packing: The Theory of Discrete Analytic Functions. Cambridge University Press, April 2005.
[9] Alexander Astrom and Christoffer Astrom: Circular knotworks consisting of pattern no. 295: a mathematical approach. Journal of Mathematics and the Arts, 5(4):185–197, November 2011.
[10] Walter Crum Watson. Portuguese architecture. A. Constable and company, limited, 1908.
Links
Full Text
http://archive.bridgesmathart.org/2012/bridges2012-133.pdf
