Geometry is from the Greek geômetria (from gê "earth, land" + -metria "measuring"), which means "earth measure as in surveying the land" [Hoad 1996, Liddell 1940, Simpson 1989]. Herodotus believed the Greeks imported it from Egypt, where its was used to calculate lands that were lost to the annual flooding of the Nile [Herodotus 1998 II, 109, 136]. In fact, geometry dates to our ability to count and to translate number into spatial pattern. It appears in prehistoric structures and is practiced everywhere by children at play.
Geometry as a technique for spatial organization evolved in western culture from ancient Egyptian sages and surveyors and from Greek philosophers. It was preserved by master builders of Gothic cathedrals and later revived by humanists and artists of the Renaissance. It continues to influence the way we see the world today.
Geometry informs the perennial question of unity in a complex
world. Regular geometric figures -- the triangle, the square,
and the pentagon -- contain specific ratios and proportions which
can mediate diverse elements and quantities. We will set aside
questions of whether or when such proportions were applied historically
to architecture and art, or whether geometric patterns are divinely
inspired, fixed within the natural world, or imposed from without
by human perception and intelligence. Our purpose is to explore
how such proportions enable architects, designers and artists
to accomplish unified schemes from a diversity of elements.
But symmetry can be synonymous with "proportion," which means "the harmonious relation of parts to each other or to the whole." The Greek for mathematical proportion is analogia, from logos, which may mean computation, relation, principle and the word, as in the expression of inward thought. Proportion is from the Latin proportionem, "comparative relation, analogy, which is adapted from proportione, in respect of ones share. [Liddell 1940, Simpson 1989]. Symmetry that is "proportional" or "relational" presumes a unified world in which unique differences may be preserved, yet integrated. It organizes space according to mutually related parts and whole.
Incommensurable proportions inherent in regular geometric figures are uniquely suited to patterns of "relational" symmetry. Let us explore such proportions through elementary geometric constructions.
Image: The Wilson A. Bentley (1865-1931) collection
of photomicrographs of snow
Hoad, T. F., ed. 1996. The Concise Oxford Dictionary of English Etymology. Oxford Reference Online. Oxford: Oxford University Press. http://www.oxfordreference.com
Liddell, Henry George and Robert Scott, eds 1940. A Greek-English Lexicon. Henry Stuart Jones, rev. Oxford: Clarendon Press. Perseus Digital Library Project. Gregory R. Crane, ed. Medford, MA: Tufts University. 2005. http://www.perseus.tufts.edu
Simpson, John and Edmund Weiner, eds. 1989. The Oxford English Dictionary. 2nd ed. OED Online. Oxford: Oxford University Press. 2004. http://www.oed.com/
Copyright ©2005 Kim Williams Books