Robert Williams (geometer)

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For other people named Robert Williams, see Robert Williams (disambiguation).
Robert Edward Williams
California State University Northridge
McDonnell-Douglas Advanced Research Laboratories, Southern Illinois University
, Eudaemon Institute, Mandala Design Associates.

Robert Edward Williams (born 1942) is an American designer, mathematician, and architect. He is noted for books on the

desert tortoises
.

Biography—life, theories, and work

Robert Williams was born in

Cincinnati, Ohio, the son of Robert Finley Williams and Edna Rita Brotherton.[1] 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.

cluster domes
An example of a clustered triangulated structure based upon small circuit principles of Catenatic Geometry.

Williams's work was originally inspired by the design principles in natural structure systems promoted by

geodesics, as Fuller had designed into geodesic dome structures.[3] 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.[citation needed
]

Williams met astronomer,

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.[4] The first of four editions of his structural geometry research was published by DARL in 1969, with the title:Handbook of Structure.[5] His paper in the journal Science proposed that his discovery of the β-tetrakaidecahedron is the most reasonable alternative[6] to Lord Kelvin's α-tetrakaidecahedron.[7]

tetrakai
Topological transformation from the Lord Kelvin α-tetrakaidecahedron (a) to the Williams β-tetrakaidecahedron (c), having 8 pentagons, 4 hexagons, and 2 square faces.

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.[8]
In the spring of 1970, Williams became a visiting lecturer in Design at
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.

Environmental design work

Fort Irwin Military Reservation and Edwards Air Force Base in California, USA.[15][16][17][18] Of all of Williams' design and architectural work, he considers his association with biologists, David Morafka[19] and Kenneth Nagy to repopulate the Western Mojave Desert with the desert tortoise as his most rewarding environmental design work.[20]

Catenatic Geometry and Sacred Geometry

In both his books and lectures, Williams is a keen popularizer of the geometries in natural structures and how they can be used in environmental design. His current work focuses on two concepts first introduced in Natural Structure: Toward a Form Language.

Catenatic Geometry

Following the lead of mathematicians

fundamental forces, discrete units of space, and the expansion of the universe
.

Photo of intersecting small circuit boundaries that form the conceptual basis for Catenatic Geometry.
One of six Cosmology Charts: Law of Seven

Sacred Geometry

From the beginning of his geometry research, Williams considered polyhedral geometry as the basis of a Form Language comprising three levels: the Formative (geometry), the Purportive (psychology), and the Symbolic. With respect to the symbolic Level, he followed the lead of

seasons
of the year, among others. The relationships are depicted in six integrated cosmology charts.

Publications

  • 1967. Geometry, Structure, Environment. Masters Thesis. Carbondale: Southern Illinois University.
  • 1968. Handbook of Structure. McDonnell-Douglas Advanced Research Laboratories. Research Communication 75.
  • 1972. Natural Structure: Toward a Form Language. Moorpark, California: Eudaemon Press.
  • 1978. The Geometrical Foundation of Natural Structure. New York: Dover Publications, Inc.
    ISBN 0-486-23729-X
    .
  • 2009. The Geometry of Natural Structure (40th Anniversary Edition). San Francisco: Eudaemon Press.
    ISBN 978-0-9823465-1-8
  • 2009. The Kiss Catenatic: The Introduction of Catenatic Geometry and its Environs. San Francisco: Eudaemon Press.
    ISBN 978-0-9823465-2-5
  • 2009. The Integration of Universal Constants. San Francisco: Eudaemon Press.
    ISBN 978-0-9823465-0-1
    .
  • 2020. Concealed Symmetry: Modulators Within Universal Process. Santa Paula: Eudaemon Press.
    ISBN 978-0-9823465-5-6
    .

References

  1. ^ Wall Lake Blade (Iowa) newspaper archives, Jan. 9, 1942, p.4
  2. ^ Buckminster Fuller Institute. (http://www.bfi.org/)
  3. ^ Williams, R. Geometry, Structure, Environment. Masters Thesis: Southern Illinois University, 1967.
  4. ^ Schefter, J. "On Base in Space," Pop. Sci. 3/89, pp. 94-98
  5. ^ Kantor, J. "Handbook of Structure." Whole Earth Catalog. Spring 1970, p. 30.
  6. ^ Williams, R. "Space-Filling Polyhedron: Its Relation to Aggregates of Soap Bubbles, Plant Cells, and Metal Crystallites". Science 161, 2762–77 (1968).
  7. ^ Thompson, W (Lord Kelvin). "On the Division of Space with Minimum Partitional Area". London, Edinburgh & Dublin Phil. Mag. & Jour. Sci., 24. 5035–14 (1887).
  8. ^ Whyte, Wilson, and Wilson eds. Hierarchical Structures. New York: American Elsevier Publishing Co., 1969.
  9. ^ Nicely, M. "Designer's Target: People Problems" Daily Egyptian, v. 50, No. 127, 26 April 1969, p. 1
  10. ^ Fuller, Buckminster. Synergetics. New York: MacMillan Publishing. 1975. p.876
  11. ^ 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.
  12. ^ Komori, V. The Broad Perspective. Radio interview with Robert Williams: Geometer, Cosmologist, Architect: “The Geometric reminder of our interconnectedness and place in our Universe.” 9/11/2009.
  13. ^ "Buildings from Nature", Industrial Research, pp. 24–5, June 1968
  14. ^ "New Beginnings," E.A.T. News (6/1/67). Vol. 1, No. 2, p. 3
  15. ^ Chavez, S. "Modular habitat may aid threatened tortoise population." Antelope Valley Press. 3/22, 2001. p. 1
  16. ^ Skeen, J. “Pens Help Save Baby Tortoises Species is Threatened”. Daily News. (Los Angeles, California) May 9, 2005
  17. ^ McGovern, M. “Shell Shocked: Head Start Program Aims to Bolster Tortoise Population.” Airman Magazine. 8/27/2009.
  18. New York Times
    . February 21, 2010.
  19. ^ Morafka, D., Berry, K., Spangenberg, E. "Predator-Proof Field Enclosures for Enhancing Hatching Success and Survivorship of Juvenile Tortoises: A Critical Evaluation." In: Van Abbema, J., ed. Conservation, Restoration, and Management of Tortoises and Turtles. New York Turtle and Tortoise Society. pp. 147–65.
  20. ^ Williams, R. "The Evolution and Design of the Ars-Vivant Wildlife Protector system for Use in Raising Neonate Desert Tortoises." Proceedings of the 2002–2003 Symposia of the Desert Tortoise Council. Pp. 53–9.
  21. ISBN 0-500-81030-3

U. S. Patent Office publications

  • "Shelter system of clustered modular enclosures". U.S. Patent 6,532,701 (March 18, 2003).
  • "A Unified Method and System for Multi-Dimensional Mapping of Spatial-Energy Relationships Among Micro- and Macro-Events in the Universe". U.S. Patent Application No. 10/714,142, Publication No. US-2005-0143919-A1 (June 30, 2005).

External links
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