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Robert Edward Williams (born 1942) is an American designer, mathematician, and architect. He is noted for books on the geometry of natural structure, the discovery of a new space-filling polyhedron, the development of theoretical principles of Catenatic Geometry, and the invention of the ''Ars-Vivant Wild-life Protector System'' for repopulating the Western Mojave Desert in California, USA with desert tortoises. ==Biography—life, theories, and work== Robert Williams was born in Cincinnati, Ohio, the son of Robert Finley Williams and Edna Rita Brotherton.〔''Wall Lake Blade'' (Iowa) newspaper archives, Jan. 9, 1942, p.4〕 His father was the oldest member of the Williams Brothers, a quartet of musical entertainers, who appeared on recordings, radio, and television, from the late 1930s to the present. Williams's work was originally inspired by the design principles in natural structure systems promoted by R. Buckminster Fuller. He was introduced to the work of Fuller by designer Peter Pearce in 1963. He finished graduate studies in structural design at Southern Illinois University in 1967, where Fuller was University Professor.〔Buckminster Fuller Institute. (http://www.bfi.org/)〕 While at SIU, he invented a system of clustering dome structures by using small circle Catenatic Geometry principles rather than great circles, or geodesics, as Fuller had designed into geodesic dome structures.〔Williams, R. ''Geometry, Structure, Environment''. Masters Thesis: Southern Illinois University, 1967.〕 From his research with naturally packed cell systems (biological cells, soap bubble packings, and metal crystallites) he also discovered a new space-filling polyhedron, the β-tetrakaidecahedron, the faces of which closely approximate the actual distribution of the kinds of faces found in experimental samples of cell geometry in natural systems. Williams met astronomer, Albert George Wilson at the Rand Corporation in 1966. Wilson invited him to conduct research at the McDonnell-Douglas Corporation Advanced Research Laboratories (DARL) in Huntington Beach, California, USA. After graduate studies, he joined Dr. Wilson in September 1967 and continued his research into general structure principles in natural systems. He was the geometry and structure consultant to NASA engineer, Charles A. Willits, on the initiatory work in the development of large scale structure systems for space stations.〔 Schefter, J. "On Base in Space," Pop. Sci. 3/89, pp. 94-98〕 The first of four editions of his structural geometry research was published by DARL in 1969, with the title:''Handbook of Structure''.〔Kantor, J. "Handbook of Structure." ''Whole Earth Catalog.'' Spring 1970, p. 30.〕 His paper in the journal ''Science'' proposed that his discovery of the β-tetrakaidecahedron is the most reasonable alternative〔Williams, R. "Space-Filling Polyhedron: Its Relation to Aggregates of Soap Bubbles, Plant Cells, and Metal Crystallites". ''Science'' 161, 2762–77 (1968).〕 to Lord Kelvin’s α-tetrakaidecahedron.〔Thompson, W (Lord Kelvin). "On the Division of Space with Minimum Partitional Area". ''London, Edinburgh & Dublin Phil. Mag. & Jour. Sci.'', 24. 5035–14 (1887).〕 As an organizer and presenter at the ''First International Conference on Hierarchical Structures'' sponsored by DARL in 1968, Williams was an early proponent advocating the discipline of Hierarchical Structure to be a legitimate area of scientific research.〔Whyte, Wilson, and Wilson eds. ''Hierarchical Structures''. New York: American Elsevier Publishing Co., 1969.〕 In the spring of 1970, Williams became a visiting lecturer in Design at Southern Illinois University.〔Nicely, M. "Designer's Target: People Problems" ''Daily Egyptian,'' v. 50, No. 127, 26 April 1969, p. 1〕 A year later he returned to California, and started the design company Mandala Design Associates. In 1972, Eudaemon Press published ''Natural Structure: Toward a Form Language'', an expanded edition of the original ''Handbook of Structure''. In 1979, Dover Publications published the third edition titled, ''The Geometrical Foundation of Natural Structure'', in its series of classical explanations of science. These works are cited in many books on geometry, science, and design.〔Fuller, Buckminster. ''Synergetics.'' New York: MacMillan Publishing. 1975. p.876〕〔Weisstein, Eric W. (2003) ''CRC Concise Encyclopedia of Mathematics.'' Boca Raton, Florida: CRC Press. Pp. 301, 313, 422, 432, 708, 837, 924, 936, 1207, 1208, 1402 1432, 2196, 2303, 2306, 2524, 2573, 2718, 2761, 2841, 2963, 3114, 3163.〕 Numerous references to these works are found in geometry articles in Wikipedia and Mathworld. On the fortieth anniversary of the initial DARL publication, Eudaemon Press published a commemorative 40th anniversary edition: ''The Geometry of Natural Structure: A Language of Form Source Book for Scientists and Designers''.As a companion volume, Eudaemon Press also published Williams's recent work: ''The Kiss Catenatic: The Introduction of Catenatic Geometry and its Environs''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Robert Williams (geometer)」の詳細全文を読む スポンサード リンク
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