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".
A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes.
The Mercator projection is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. The map is thereby conformal. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation is very small near the equator but accelerates with increasing latitude to become infinite at the poles. As a result, landmasses such as Greenland, Antarctica, Canada and Russia appear far larger than they actually are relative to landmasses near the equator, such as Central Africa.
In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography.
The Dymaxion car was designed by American inventor Buckminster Fuller during the Great Depression and featured prominently at Chicago's 1933/1934 World's Fair. Fuller built three experimental prototypes with naval architect Starling Burgess – using donated money as well as a family inheritance – to explore not an automobile per se, but the 'ground-taxiing phase' of a vehicle that might one day be designed to fly, land and drive – an "Omni-Medium Transport". Fuller associated the word Dymaxion with much of his work, a portmanteau of the words dynamic, maximum, and tension, to summarize his goal to do more with less.
A world map is a map of most or all of the surface of Earth. World maps, because of their scale, must deal with the problem of projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensional surface of the Earth. While this is true of any map, these distortions reach extremes in a world map. Many techniques have been developed to present world maps that address diverse technical and aesthetic goals.
Bernard Joseph Stanislaus Cahill, American cartographer and architect, was the inventor of the octahedral "Butterfly Map". An early proponent of the San Francisco Civic Center, he also designed hotels, factories and mausoleums like the Columbarium of San Francisco.
In cartography, a conformal map projection is one in which every angle between two curves that cross each other on Earth is preserved in the image of the projection; that is, the projection is a conformal map in the mathematical sense. For example, if two roads cross each other at a 39° angle, their images on a map with a conformal projection cross at a 39° angle.
The Geoscope was a proposal by Buckminster Fuller around 1960 to create a 200-foot-diameter (61 m) globe that would be covered in colored lights so that it could function as a large spherical display. It was envisioned that the Geoscope would be connected to computers which would allow it to display both historical and current data, and enable people to visualize large scale patterns around the world. Several projects by his students to build a "miniature Earth", starting with a 20-foot version at Cornell University in 1952, were precursors of the Geoscope proposal. Before proposing the Geoscope, Fuller had invented the Dymaxion map, a novel map projection for the whole Earth.
The Waterman "Butterfly" World Map is a map projection created by Steve Waterman. Waterman first published a map in this arrangement in 1996. The arrangement is an unfolding of a polyhedral globe with the shape of a truncated octahedron, evoking the butterfly map principle first developed by Bernard J.S. Cahill (1866–1944) in 1909. Cahill and Waterman maps can be shown in various profiles, typically linked at the north Pacific or north Atlantic oceans.
The Cahill–Keyes projection is a polyhedral compromise map projection first proposed by Gene Keyes in 1975. The projection is a refinement of an earlier 1909 projection by Bernard Cahill. The projection was designed to achieve a number of desirable characteristics, namely symmetry of component maps (octants), scalability allowing the map to continue to work well even at high resolution, uniformity of geocells, metric-based joining edges, minimized distortion compared to a globe, and an easily understood orientation to enhance general usability and teachability.
Shoji Sadao was a Japanese American architect, best known for his work and collaborations with R. Buckminster Fuller and Isamu Noguchi. During World War II he was stationed in Germany and was a cartographer for the U.S. Army.
AuthaGraph is an approximately equal-area world map projection invented by Japanese architect Hajime Narukawa in 1999. The map is made by equally dividing a spherical surface into 96 triangles, transferring it to a tetrahedron while maintaining area proportions, and unfolding it in the form of a rectangle: it is a polyhedral map projection. The map substantially preserves sizes and shapes of all continents and oceans while it reduces distortions of their shapes, as inspired by the Dymaxion map. The projection does not have some of the major distortions of the Mercator projection, like the expansion of countries in far northern latitudes, and allows for Antarctica to be displayed accurately and in whole. Triangular world maps are also possible using the same method. The name is derived from "authalic" and "graph".
The Lee conformal world in a tetrahedron is a polyhedral, conformal map projection that projects the globe onto a tetrahedron using Dixon elliptic functions. It is conformal everywhere except for the four singularities at the vertices of the polyhedron. Because of the nature of polyhedra, this map projection can be tessellated infinitely in the plane. It was developed by L. P. Lee in 1965.
The Strebe 1995 projection, Strebe projection, Strebe lenticular equal-area projection, or Strebe equal-area polyconic projection is an equal-area map projection presented by Daniel "daan" Strebe in 1994. Strebe designed the projection to keep all areas proportionally correct in size; to push as much of the inevitable distortion as feasible away from the continental masses and into the Pacific Ocean; to keep a familiar equatorial orientation; and to do all this without slicing up the map.
In geodesy, a map projection of the triaxial ellipsoid maps Earth or some other astronomical body modeled as a triaxial ellipsoid to the plane. Such a model is called the reference ellipsoid. In most cases, reference ellipsoids are spheroids, and sometimes spheres. Massive objects have sufficient gravity to overcome their own rigidity and usually have an oblate ellipsoid shape. However, minor moons or small solar system bodies are not under hydrostatic equilibrium. Usually such bodies have irregular shapes. Furthermore, some of gravitationally rounded objects may have a tri-axial ellipsoid shape due to rapid rotation or unidirectional strong tidal forces.
In map projections, an interruption is any place where the globe has been split. All map projections are interrupted at at least one point. Typical world maps are interrupted along an entire meridian. In that typical case, the interruption forms an east/west boundary, even though the globe has no boundaries.
Snyder equal-area projection is a polyhedral map projection used in the ISEA discrete global grids. It is named for John P. Snyder, who developed the projection in the 1990s.
A polyhedral map projection is a map projection based on a spherical polyhedron. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon or other shape in the plane. The best-known polyhedral map projection is Buckminster Fuller's Dymaxion map. When the spherical polyhedron faces are transformed to the faces of an ordinary polyhedron instead of laid flat in a plane, the result is a polyhedral globe.
