R. Buckminster Fuller's Elementary Geometries
1. Elementary Geometries
Geometry is a branch of mathematics concerned with figures and deal with questions of their shape, size and relative position. Further explorations of geometry also deal with properties of space. Geometry is considered to be one of the oldest sciences, with earliest recorded beginnings developed in ancient Egypt, Mesopotamia, and the India as early as 3000 BC.
Presumably in 3rd century BC, Euclid, a prominent Ancient Greek mathematician, systemized available body of knowledge on figures and own developments in treatise named “Elements” consisting of 13 books. Although many of the theories included in Euclid's “Elements” were developed and discussed by earlier mathematicians, Euclid's “Elements” represents the earliest known systematic discussion of this subject, which has been one of the most influential works in science. This work is also valuable as a methodological guide, as Euclid showed how a small set of intuitively appealing axioms can be fit together into a comprehensive deductive and logical system, proving many other propositions (theorems).
For more than two thousand years, the term “Geometry” was applied to the Euclid’s development and later derivatives of his work. Only in 19th century such prominent scientists such as Gauss, Bolyai, and Lobachevsky, demonstrated that properties of space, as set out in conventional, Euclidean geometry, represent only one possibility. Since then, geometry is often divided into two broad classes: Euclidean Geometry (also referred to as Ordinary Geometry or Elementary Geometry) and non-Euclidean Geometry. Although non-Euclidean geometries are an important step for the science, Euclidean geometry and its derivatives is dominantly important for architecture and design.
Traditional architecture is primarily based on conventional rectangles and in small degree makes use of other geometric elements. However, as example of Buckminster Fuller and his followers shows, it is not the only option.
Fuller explored the properties of new geometries in the building design. Fuller’s famous geodesic domes represent lattice shell structure, which can provide required rigidness and stability, while being light. The core principle behind this design is tensegrity (“tensional integrity”) being ability of the structure to maintain integrity due to synergy between balanced tension and compression of its elements. Elements of this structure may be tetrahedrons, octahedrons and other 3-D elements packing closely to form a sphere. Notably, these elements can be formed by even simpler (more “elementary”) geometries, such as triangles, which contributes to the properties of these forms. Properties of these elementary geometries, has been studied by scientists for many centuries, however ability to create more complex, yet simple, design with outstanding properties was to the large extend overlooked. Fuller in his search for alternative solutions in architectural design, explored synergy between elements, which lead to invention of such innovative solution as geodesic domes and related designs. In his studies, Fuller often went beyond architecture, considering synergy being one of the Universal principles with many applications.
2. R. Buckminster Fuller
Richard Buckminster Fuller (July 12, 1895 – July 1, 1983) was a prominent American architect, designer, inventor, author, and futurist. Fuller developed numerous inventions, mostly related to architectural designs, among which probably the best known is the Geodesic Dome. He published more than thirty books, on architectural design, science and philosophy.
Richard Buckminster Fuller (July 12, 1895 – July 1, 1983) was a prominent American architect, designer, inventor, author, and futurist. Fuller developed numerous inventions, mostly related to architectural designs, among which probably the best known is the Geodesic Dome. He published more than thirty books, on architectural design, science and philosophy.
He was born on July 12, 1895, in Milton, Massachusetts. Much of his youth he spent on Bear Island, Maine, where he demonstrated his natural talent and love to designing and construction, for example he experimented with designing a new mechanism for small boat propulsion by a person. For his experiments often used materials found in woods and sometimes constructed required tools himself. Later, Fuller admitted that his early age experiments not only provoked interest in design in him, but developed a habit of getting familiar and knowledgeable with properties of materials, which aided in his later projects (Pawley 1990).
He often made items from materials he brought home from the woods, and sometimes made his own tools. He experimented with designing a new apparatus for human propulsion of small boats.
In 1913, at the age of 18, Fuller, in line with family tradition, was sent to study in Harvard. However, Fuller demonstrated disinclination for orthodox education and was expelled for irresponsibility and packed off to Canada to a group of cotton-mill machine fitters, which he did with great enthusiasm. He was returning to Harvard, as a result of his diligence, but was expelled again for sustained lack of interest. He abandoned formal education and start working at Armour & Company in various New York and New Jersey branches, where he started with lugging beef. Eventually, studying refrigeration, marketing and accounting he received the post of assistant cashier in two years.
During World War I Fuller succeeded to be accepted for the Navy in 1917, at the age of 22, where he served for two years till 1919. In Navy he enjoyed dealing with ballistics, navigation and the mass tonnage movements logistics, which required applied knowledge of mathematics. There he made his first two practical inventions: a seaplane rescue mast and boom and the design conception of a vertical take-off aircraft. After army, he continued his on job education in meat packing industry, acquiring experience in management. And in 1922 together with his father-in-law, he founded a company producing innovative fibrous concrete building blocks for construction of light-weight, weatherproof, and fireproof housing. However, this company failed and by the age of 32, in 1927, Fuller became bankrupt (Pawley 1990). Bankruptcy and death of his daughter lead him to alcohol abuse and depression. However, at some point, he decided to embark on "an experiment, to find what a single individual [could] contribute to changing the world and benefiting all humanity" (Patton 2008).
The year 1927 becomes the central pivot of Fuller's life. He publishes "4D" and "4D Timelock" essays. These publications sum up Fuller’s massive intellectual stocktaking at this time as he outlines many of the basic propositions of his future design philosophy. Notably, Fuller demonstrates comprehensive and elaborate approach: each of the developments proposed by him is based on considerations of deep, most universal context, and only then goes details. One of the most remarkable illustrations in "4D Timelock" is a “World Town Plan sketch”. This sketch presents multi-deck housings located around the globe, forming a global shelter service maintained by air. Fuller underlined that underlines that solutions for world housing problem must embrace universal requirements, satisfying a broad range of human functions. Fuller housing design was lightweight, i.e. required less materials, and cheap, according to his calculation, standard twelve-deck version should weight 45 tons (including even such auxiliaries as swimming pool, gymnasium, library decks and accessories) at a cost of $23 thousand, if mass-produced (McHale 1962). Needless to say that such solution was and is still quite ahead of its time. But Fuller believed that the volume of production required to meet current and future demand can only be achieved through quite advanced scientific and industrial solutions (McHale 1962). After two years of designing some of his concepts were implemented in the prototypes.
During his middle period of (1927-46) Fuller focused on the theme of studies in structural principles, industrialized housing, logistics and economic planning (macro level), with respect to realization of his housing ideas. Simultaneously with his research and practical studies, Fuller lectured and worked in different. In late 1944, he served in U.S. Foreign Economic Administration and there he developed a plan for the postwar conversion of the aircraft industry for housing construction purposes.
In 1949 Fuller completed construction of his first geodesic dome – an icosahedron building with diameter of 4.3 meters made of aluminum aircraft tubing and a vinyl-plastic skin. Importance of his work was recognized by the U.S. government and employed he was employed to make small domes for the army. Fuller managed construction of thousands of such domes around the globe for a few following years.
For almost a half of the century since his first dome construction, Fuller developed many ideas, inventions and designs in the field of practical and cheap shelters and transportation. He received international recognition after construction of a huge geodesic domes during the 1950s. Fuller lectured for many years around the world and taught in various universities, notably in Washington University in St. Louis (1955-59) and Southern Illinois University Carbondale (1959 to 1970). He received many honorary doctorates and in 1968 he gained full professorship in the School of Art and Design. His developments and publication with respect to the future of the humanity lead to a recognition as a Humanist of the Year in the 1969 by American Humanist Association. In 1983 he received the Presidential Medal of Freedom presented by President Ronald Reagan.
Fuller died at the age of 87, on July 1, 1983, being widely acknowledged as guru of the architecture, design, futurism and 'alternative' communities.
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