Sections Beyond Golden
Inhaltsverzeichnis
Reference
Peter Steinbach: Sections Beyond Golden. In: Bridges 2000. Pages 35–44
DOI
Abstract
Over the centuries, the Fine Arts have celebmted seveml special. numerical ratios and proportions for their visual dynamics or balance and sometimes for their musical potential. From the golden ratio to the sacred cut, numerical relationships are at the heart of some of the greatest works of Nature and of Western design. This article introduces to interdisciplinary designers three newly-discovered numerical relations and summarizes current knowledge about them~ Together with the golden ratio they form a golden family, and though not well understood yet, they are very compelling, both as mathematical diversions and as design elements. They also point toward an interesting geometry problem that is not yet solved. (Some of these ideas also appear in [5] in more technical language.)
Extended Abstract
Bibtex
Used References
[1] E. J. Dijksterhuis, Archimedes. Copenhagen: Ejnar Munksgaard, 1956.
[2] Le Corbusier, The Modulor. Cambridge: Harvard University Press, 1954.
[3] Robert Lawlor, Sacred Geonetry. London: Thames & Hudsm, 1992.
[4] P. H. Scholfield, The ThtDry of Proportion in Architecture. Cambridge: The University Press, 1958.
[5] Peter Steinbach, Golden Fields: A Case for the Heptagon. MAA Mathematics Magazine, February 1997.
[6] Kim Williams, The Sacred Cut Revisited: The Pavement of the Baptistery of San Giovanni, Florence. The Mathematical Intelligencer 16:2 (1994) 18.
GyOrgy Doczi, The Power of Limits. Boulder: Shambala, 1981.
Matila Ghyka, The Geometry ofArt and Life. New York: Dover, 1978.
Grünbaum & Shephard, Tilings and Patterns. New York: Freeman and Co., 1987.
Jonathan Hale, The Old Way of Seeing. New York: Houghtm Mifflin, 1994.
Jay Hambidge, The Elements ofDynamic Symmetry. New Haven, 1948.
Gyorgy Kepes, Module, Proportion, Symmetry, Rhythm. New York: GeorgeBraziller, 1966.
Nelson, Joseph, & Williams, Multicultural Mathematics. Oxford University Press, 1993.
Dan Pedoe, Geometry and the Visual Arts. New Yak: Dover,1976.
Links
Full Text
http://archive.bridgesmathart.org/2000/bridges2000-35.pdf
