Systems of Proportion in Design and Architecture and their Relationship to Dynamical Systems Theory
Inhaltsverzeichnis
Reference
Jay Kappraff: Systems of Proportion in Design and Architecture and their Relationship to Dynamical Systems Theory. In: Bridges 1999. Pages 27–40
DOI
Abstract
A general theory of proportion is presented and applied to proportional systems based on the golden mean, root 2, and root 3. These proportions are shown to be related to regular star polygons and to the law of repetition of ratios. The additive properties of these proportions are presented in terms of both irrational and integer series. The geometrical and number theoretic properties of the root 3 system are focused on since this system has not been previously reported in the literature. An architectural Rotunda is presented. The relationship between systems of proportion and the symbolic dynamics of chaos theory is presented.
Extended Abstract
Bibtex
Used References
Chen, H., Li, D.x., and Kuo, K.H. "New type of two-dimensional quasicrystal with twelvefold rotational symmetry." Phys. Rev. Lett. 60, ppI645-1648.
Coxeter, H.S.M. Regular Polytopes. New York: Dover (1973).
Edwards, E. B. Pattern and Design with Dynamic Symmetry. Originally published as Dynamarhythmic Design (1932) (rpt. New York: Dover 1968).
Hambridge, J. The Elements of Dynamic Symmetry. Originally pyublished by Brentano's (1929) (rpt. by New York: Dover).
Kappraff, J. Connections: The Geometric Bridge between Art and Science. New York: McGraw-Hill (1991).
Kappraff, 1. "Musical Proportions at the Basis of Systems of Proportion Both Old and New." In Nexus: Architecture and Mathematics edited by K. Williams. Fececchio, Italy: Edizioni Dell'Erba (1996a).
Kappraff, J. "Linking the Musical Proportions of the Renaissance with the Modulor of Le Corbusier and the System of Roman Proportions." International Journal of Space Structures, Vol. 11, No. 1 and 2 (1996b).
Kappraff, J. Mathematics Beyond Measure. New York: Plenum Press (in press).
Le Corbusier. Modulor. Cambridge: MIT Press (1968).
Mitrovic,B. "Palladio's theory of Proportions and the Second Book of the Auattro Libri dell' Architettura." Journal ofthe Soc. of Arch. Rist. 49, 3 pp 281-285 (Sept. 1990).
Nicholson, B., Kappraff, J., and Hisano, S. "A Taxonomy of Ancient Geometry and the Hidden Pavements of the Laurentian Library." Proceedings, Bridges: Mathematical Connections in Art, Music, and Science, edited by Reza Sarhangi, PP 255-271 (1998)
Schroeder, M. Fractals, Chaos, Power Laws. New York: W.R. Freeman (1991).
De Spinadel, V.W. From the Golden Mean to Chaos. Self published ISBN 950-43-9329-1 (1998).
Vakil, R. A Mathematical Mosaic - Patterns and Problem Solving. Burlington, Ontario: Brendan Kelly Publ. Inc. (1996).
Wassell, S.R. "The Mathematics of Palladio's Villas." In Nexus: Architecture and Mathematics. Fuccechio: Edizioni Dell'Erba (1998).
Wang, N., Chen, H., and Kuo, L.R. "Two dimensional quasicrystal with eight-fold rotational symmetry." Phys. Rev. Lett. 59, pp 1010-1013.
Williams, K. "Michelangelo's Medici Chapel: the cube, the square and the -../2 rectangle." Leonardo. Vol 30, No.2 (1997).
Wittkover, R. Architectural Principles in the Age of Ruman ism. New York: Norton (1971).
Links
Full Text
http://archive.bridgesmathart.org/1999/bridges1999-27.pdf
