On Growth and Form in Nature and Art: The Projective Geometry of Plant Buds and Greek Vases
Inhaltsverzeichnis
Reference
Stephen Eberhart: On Growth and Form in Nature and Art: The Projective Geometry of Plant Buds and Greek Vases. In: Bridges 2000. Pages 267–278
DOI
Abstract
D' Arcy Thompson's pioneering book On Growth and Form showed how a square grid could be laid over the profile of one species of animal and then made to fit that of another related animal by a suitable deformation of space, thus allowing e.g. the shapes of missing bones to be estimated when reconstructing the fossil skeleton of an unknown species. Where Thompson had resorted to quite arbitrary spatial distortions for his examples, George Adams realized that the kind of conformal maps first discussed by Felix Klein (collineations of plane and space with invariant "path curves") would fit at least certain parts of plants and animals by conservative means, being in effect linear transformations in a non-Euclidean setting. This was then extended by Lawrence Edwards to quad- ratic models, showing how certain pairs of parts of a given plant or animal can be formally related in a species-true manner. I have applied these approaches to Greek amphora:, showing how their body and base and/or neck shapes are similarly related.
Extended Abstract
Bibtex
Used References
Stephen Eberhart. "Some Briggsian Bridges between Sense Perception, Postage Stamps, and Stylized Propor- tions," Proceedings of 2m Bridges Conference in Winfield, KS, 1999.
Albrecht DUrer, The Painter's Manual (Nfunberg, 1525) translated and commented by Walter L. Strauss, Abatis Books, New York, 1977.
Albrecht DUrer, Vier BUcher von menschlicher Proportion, facsimile of 1st edition (Niirnberg, 1528), G.M. Wagner, London, 1970.
D' Arcy Thompson, On Growth and Form (1917), abridged edition, Cambridge University Press, 1961.
Louis Locher-Ernst, Raum und Gegenraum (1957), 2m edition, Philos.-Anthropos. Verlag am Goetheanum, Dornach, 1970.
Louis Locher-Ernst, Geometrische Metamorphosen (1947-1955), Philos.-Anthropos. Verlag am Goetheanum, Dornach, 1970.
George Adams, Strahlende Weltgestaltung, Math.-Astron. Sektion am Goetheanum, Dornach, 1934.
Felix Klein, Vorlesungen iiber nicht-euklidische Geometrie (1892), 1928 edition, reprinted by Springer Ver- lag, Berlin, 1968.
Felix Klein, Vorlesungen iiber hOhere Geometrie (1893), 1926 edition, reprinted by Springer Verlag, Berlin, 1968.
Lawrence Edwards, Projective Geometry, Rudolf Steiner Institute, Phrenixville, 1982.
Lawrence Edwards, The Field of Form, Floris Books, Edinburgh, 1982.
Lawrence Edwards, The Vortex of Life, Floris Books, Edinburgh, 1993.
Stephen Eberhart, "Grecian Amphorre as Path-Curve Shapes," Math.-Phys. Correspondence, No. 27, 1979.
Links
Full Text
http://archive.bridgesmathart.org/2000/bridges2000-267.pdf
