Bourgoin's 14-Pointed Star Polygon Designs
Inhaltsverzeichnis
Reference
B. Lynn Bodner: Bourgoin's 14-Pointed Star Polygon Designs. In: Bridges 2010. Pages 135–142
DOI
Abstract
In this paper we explore a contemporary conceptualization and creation of four, historical 14-pointed star polygon designs illustrated and analyzed in Plates 164 – 167 of Bourgoin’s Arabic Geometrical Pattern and Design [1]. We seek to determine how the original designer of these patterns may have determined, without mensuration, the proportion and placement of the star polygons comprising each pattern. We will do this by proposing a plausible Euclidean “point-joining” compass-and-straightedge reconstruction for each.
Extended Abstract
Bibtex
Used References
[1] Bourgoin, J. (1973). Arabic Geometrical Pattern and Design, Dover Publications. Original 1879.
[2] The Geometer’s Sketchpad software program, available at http://www.keypress.com.
[3] Abu’l-Wafā’ al-Buzjani (10th Century). Kitāb fimāyahtāju ilayhi al-sāni‘min a‘māl al-handasa (About that which the artisan needs to know of geometric constructions).
[4] Sarhangi, R. (2007). “Geometric Constructions and their Arts in Historical Perspective,” Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, pp. 233-240.
[5] Berggren, J.L. (1986). Episodes in the Mathematics of Medieval Islam, Springer, pp. 77-82.
[6] Hogendijk, J.P. (1984). “Greek and Arabic Constructions of the Regular Heptagon,” Archive for History of Exact Sciences 30, 197-330.
[7] McBurney, S. (2008). “Mathematical Secrets of Seven,” Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, pp. 417-420.
[8] Microsoft Paint software program.
[9] Pattern in Islamic Art: The Wade Photo Archive, available at http://www.patternsinislamicart.com
[10] Necipoğlu, Gülru (1995). The Topkapı Scroll – Geometry and Ornament in Islamic Architecture: Topkapı Palace Museum Library MS H. 1956, Santa Monica, California: The Getty Center for the History of Art and Humanities.
Links
Full Text
http://archive.bridgesmathart.org/2010/bridges2010-135.pdf
