Number Theory and Art

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Reference

Vera W. de Spinadel: Number Theory and Art. In: Bridges 2003. Pages 415–422

DOI

Abstract

The Metallic Means Family (MMF), was introduced by the author [1], as a family of positive irrational quadratic numbers, with many mathematical properties that justify the appearance of its members in many different fields of knowledge, including Art. Its more conspicuous member is the Golden Mean. Other members of the MMF are the Silver Mean, the Bronze Mean, the Copper Mean, the Nickel Mean, etc.

Extended Abstract

Bibtex

Used References

1] Spioadel Vera W. de, From the Golden Mean to chaos, Nueva Librerfa, Buenos Aires, Argentina, 1998.

[2] Kepler Johannes, Mysterium Cosmographicum de admirabili proportione orbium celestium, 1596.

[3] Plato, Timaeus. D. Lee (trans.), New York: Penguin, 1977.

[4] Hawkins Gerald S., Stonehenge decoded, edition Dell Publishing Co. New York, 1965.

[5] Hambidge Jay, The elements oj Dynamic Symmetry, Dover Publications Inc., 1967.

[6] Soroko Eduard M., Golden code oj NeJertiti's Image, ISIS Fourth International Conference, Technion, Haifa, Israel, September 1998.

[7] Lund F. M., Ad Quadratum. In English (Batsford) and French (A. Morance) editions. Also Ad Quadratum II in Norwegian, 1921.

[8] Zeisiog Adolph, Aesthetische Forschungen, 1855.

[9] Le Corbusier, EI Modulor. Ensayo sobre una medida armOnica a la escala humana aplicable universalmente a la arquitectura y a la mecanica y Modulor 2 (1955). Los usuarios tienen la palabra. Continuaci6n de EI Modulor (1948). EditorialPoseid6n, Barcelona, Espana, 1976.

[10] Kappraff Jay, Musical proportions at the basis oj systems oj architectural proportion, NEXUS - Architecture and Mathematics, edited by Kim Williams, pp. 115-133, 1996.

[11] Brunes Tons, The secrets oj ancient Geometry and its use, Copenhagen: Rhodos Int. Science Publishers, 1967.

[12] Gumbs G. And Ali M. K., Dynamical maps. Cantor spectra and 10calizationJor Fibonacci and related quasiperiodic lattices, Phys. Rev. Lett. 60, Nr 11, 1081-1084, 1988.

[13] Kohmoto M., Entropy functionJor Multifractals, Phys. Rev. A37: 1345-1350, 1988.

[14] EI Naschie M. S., Silver Mean Hausdorff dimension and Cantor sets, Chaos, Solitons & Fractals 4: 1862-1870, 1994.

[15] Kolmogorov A. N., On the preservation oj quasiperiodic motions under a small variation oj Halmilton'sfunction, Dokl. Akad. Nauk. USSR 98: 525,1954.

[16] Arnold V. I., Smalls denominators and the problem oj stability oj motion in classical and celestial Mechanics, Russ. Math. Surv. 18: 85-191, 1963.

[17] Moser J., Convergent series expansions oj quasiperiodic motions,. Math. Zeit. 33: 505-5433, 1931.


Links

Full Text

http://archive.bridgesmathart.org/2003/bridges2003-415.pdf

intern file

Sonstige Links

http://archive.bridgesmathart.org/2003/bridges2003-415.html