Robert Edward Williams | |
---|---|
Born | 1942 |
Alma mater | California State University Northridge Southern Illinois University |
Scientific career | |
Fields | Designer, Mathematician, Architect |
Institutions | 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 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.
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.
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. [2] 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. [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, 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. [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]
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 Southern Illinois University. [9] A year later he returned to California, and started the design company Mandala Design Associates.[ citation needed ] 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. [10] [11] 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.
Williams uses the geometry of Natural Structure, Catenatic Geometry principles, and Symbolic analysis as fundamental components of his architectural, environmental design, and cosmology work. [12] [13] In 1967, he became a charter member [14] of Experiments in Art and Technology(E.A.T.) founded by engineers Billy Klüver and Fred Waldhauer and artists Robert Rauschenberg and Robert Whitman. In addition to theoretical work, Williams was awarded U.S. Patent No. 6,532,701] in 2003 for a shelter system of clustered modular enclosures. He designed and constructed 18,000 square feet (1,700 m2) of these modular, moveable, expandable-contractible enclosures to raise the endangered desert tortoise (Gopherus agassizii) at the 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]
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.
Following the lead of mathematicians L. Fejes Tóth and C. A. Rogers, Williams formalized the concepts underlying Catenatic Geometry. In The Kiss Catenatic he expanded the concept of small circles covering a sphere to include interconnected platen circuits that model multi-level linked units of the 3-dimensional matrix chain. He presented examples of the use of Catenatic Geometry in discussions of dark matter and dark energy, red-shift, fundamental forces, discrete units of space, and the expansion of the universe.
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 symbologist and mythographer Robert Lawlor. [21] In The Integration of Universal Constants Williams presented relationships among numerous diverse subjects: geometric form, color spectrum, the music octave, the periodic table, astronomy, astrology, psychology, tarot, chakras, gender, seasons of the year, among others. The relationships are depicted in six integrated cosmology charts.
Richard Buckminster Fuller was an American architect, systems theorist, writer, designer, inventor, philosopher, and futurist. He styled his name as R. Buckminster Fuller in his writings, publishing more than 30 books and coining or popularizing such terms as "Spaceship Earth", "Dymaxion", "ephemeralization", "synergetics", and "tensegrity".
In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such, it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.
In geometry, a polyhedron is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
Topology is the part of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
In geometry, the truncated icosahedron is an Archimedean solid with 32 faces. It is a polyhedron that may be associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons; the Adidas Telstar was the first soccer ball to use this pattern in the 1970s. Geodesic domes such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It also corresponds to the geometry of the fullerene C60 ("buckyball") molecule. It is an example of a Goldberg polyhedron.
A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The rigid triangular elements of the dome distribute stress throughout the structure, making geodesic domes able to withstand very heavy loads for their size.
Tensegrity, tensional integrity or floating compression is a structural principle based on a system of isolated components under compression inside a network of continuous tension, and arranged in such a way that the compressed members do not touch each other while the prestressed tensioned members delineate the system spatially.
In architecture and structural engineering, a space frame or space structure is a rigid, lightweight, truss-like structure constructed from interlocking struts in a geometric pattern. Space frames can be used to span large areas with few interior supports. Like the truss, a space frame is strong because of the inherent rigidity of the triangle; flexing loads are transmitted as tension and compression loads along the length of each strut.
James Tennant Baldwin, often known as Jay Baldwin or J. Baldwin, was an American industrial designer and writer. Baldwin was a student of Buckminster Fuller; Baldwin's work was inspired by Fuller's principles and, in the case of some of Baldwin's published writings, he popularized and interpreted Fuller's ideas and achievements. In his own right, Baldwin was a figure in American designers' efforts to incorporate solar, wind, and other renewable energy sources. In his career, being a fabricator was as important as being a designer. Baldwin was noted as the inventor of the "Pillow Dome", a design that combines Buckminster Fuller's geodesic dome with panels of inflated ETFE plastic panels.
R. Buckminster Fuller coined the term design science revolution to describe his proposed scientific and socio-economic revolution accomplished by shifting from "weaponry to livingry" through the application of what he called comprehensive anticipatory design science. His World Design Science Decade, proposed to the International Union of Architects in 1961, was an attempt to catalyze the revolution.
In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes. In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum surface area than the previous best-known solution, the Kelvin structure.
In geometry, the trapezo-rhombic dodecahedron or rhombo-trapezoidal dodecahedron is a convex dodecahedron with 6 rhombic and 6 trapezoidal faces. It has D3h symmetry. A concave form can be constructed with an identical net, seen as excavating trigonal trapezohedra from the top and bottom. It is also called the trapezoidal dodecahedron.
Anne Griswold Tyng was an architect and professor. She is best known for having collaborated for 29 years with Louis Kahn at his practice in Philadelphia. She served as a professor at the University of Pennsylvania for 27 years, teaching classes in urban morphology. She was a fellow of the American Institute of Architects and an academician of the National Academy of Design. She is the first woman licensed as an architect by the state of Pennsylvania.
In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons. Much of the theory of symmetrical polyhedra is most conveniently derived in this way.
Keith Barry Critchlow was a British artist, lecturer, author, sacred geometer, professor of architecture, and a co-founder of the Temenos Academy in the UK.
Synergetics is the empirical study of systems in transformation, with an emphasis on whole system behaviors unpredicted by the behavior of any components in isolation. R. Buckminster Fuller (1895–1983) named and pioneered the field. His two-volume work Synergetics: Explorations in the Geometry of Thinking, in collaboration with E. J. Applewhite, distills a lifetime of research into book form.
Site-specific architecture (SSA) is architecture which is of its time and of its place. It is designed to respond to both its physical context, and the metaphysical context within which it has been conceived and executed. The physical context will include its location, local materials, planning framework, building codes, whilst the metaphysical context will include the client's aspirations, community values, and architects ideas about the building type, client, location, building use, etc.
Generative design is an iterative design process that uses software to generate outputs that fulfill a set of constraints iteratively adjusted by a designer. Whether a human, test program, or artificial intelligence, the designer algorithmically or manually refines the feasible region of the program's inputs and outputs with each iteration to fulfill evolving design requirements. By employing computing power to evaluate more design permutations than a human alone is capable of, the process is capable of producing an optimal design that mimics nature's evolutionary approach to design through genetic variation and selection. The output can be images, sounds, architectural models, animation, and much more. It is therefore a fast method of exploring design possibilities that is used in various design fields such as art, architecture, communication design, and product design.
A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles. They are the dual of corresponding Goldberg polyhedra, of which all but the smallest one have mostly hexagonal faces.
Victor Acevedo is an American artist best known for his digital work involving printmaking and video. He was introduced to computer graphics in 1980 while attending Gene Youngblood's survey class (based on his book Expanded Cinema) at Art Center College of Design in Pasadena, California.