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Dymaxion map

January 01, 1970

The Dymaxion map or Fuller map is a projection of a world map onto the surface of an icosahedron, which can be unfolded and flattened to two dimensions. The flat map is heavily interrupted in order to preserve shapes and sizes.

The world on a Dymaxion projection, with 15° graticule
Dymaxion projection with Tissot's indicatrix of deformation
An icosahedron, the shape the world map is projected onto before unfolding
The world flattens to a Dymaxion map as it unfolds into an icosahedron net with nearly contiguous land masses.
This icosahedral net shows connected oceans surrounding Antarctica.
Example of use illustrating early human migrations according to mitochondrial population genetics (numbers are millennia before present)
Dymaxion map of the world with the 30 largest countries and territories by total area, roughly to scale

The projection was invented by Buckminster Fuller. The March 1, 1943, edition of Life magazine included a photographic essay titled "Life Presents R. Buckminster Fuller's Dymaxion World". The article included several examples of its use together with a pull-out section that could be assembled as a "three-dimensional approximation of a globe or laid out as a flat map, with which the world may be fitted together and rearranged to illuminate special aspects of its geography".[1] Fuller applied for a patent in the United States in February 1944, showing a projection onto a cuboctahedron, which he called "dymaxion". The patent was issued in January 1946.[2]

In 1954, Fuller and cartographer Shoji Sadao produced the Airocean World Map, a version of the Dymaxion map that used a modified but mostly regular icosahedron as the base for the projection. The version most commonly referred to today, it depicts Earth's continents as "one island", or nearly contiguous land masses.

The Dymaxion projection is intended only for representations of the entire globe. It is not a gnomonic projection, whereby global data expands from the center point of a tangent facet outward to the edges. Instead, each triangle edge of the Dymaxion map matches the scale of a partial great circle on a corresponding globe, and other points within each facet shrink toward its middle, rather than enlarging to the peripheries.[3] Fuller's 1980 version of the Dymaxion map was the first definition and use of a mathematical transformation process to make the map.[4][5][6][7] It is a polyhedral map projection.

The name Dymaxion was applied by Fuller to several of his inventions.

Properties edit

Though neither conformal nor equal-area,[8] Fuller claimed that his map had several advantages over other projections for world maps.

It has less distortion of relative size of areas, most notably when compared to the Mercator projection; and less distortion of shapes of areas, notably when compared to the Gall–Peters projection. Other compromise projections attempt a similar trade-off.

More unusually, the Dymaxion map does not have any "right way up". Fuller argued that in the universe there is no "up" and "down", or "north" and "south": only "in" and "out".[9] Gravitational forces of the stars and planets created "in", meaning "towards the gravitational center", and "out", meaning "away from the gravitational center". He attributed the north-up-superior/south-down-inferior presentation of most other world maps to cultural bias.

Fuller intended the map to be unfolded in different ways to emphasize different aspects of the world.[10] Peeling the triangular faces of the icosahedron apart in one way results in an icosahedral net that shows an almost contiguous land mass comprising all of Earth's continents – not groups of continents divided by oceans. Peeling the solid apart in a different way presents a view of the world dominated by connected oceans surrounded by land.

Showing the continents as "one island earth" also helped Fuller explain, in his book Critical Path, the journeys of early seafaring people, who were in effect using prevailing winds to circumnavigate this world island.

However, the Dymaxion map can also prove difficult to use. It is, for example, confusing to describe the four cardinal directions and locate geographic coordinates. The awkward shape of the map may be counterintuitive to most people trying to use it. For example, the shortest route from Africa to South America is not obvious. Depending on how the map is projected, land masses and oceans are often divided into several pieces.

Impact edit

A 1967 Jasper Johns painting, Map (Based on Buckminster Fuller's Dymaxion Airocean World), depicting a Dymaxion map, hangs in the permanent collection of the Museum Ludwig in Cologne.[11][12]

The World Game, a collaborative simulation game in which players attempt to solve world problems,[13][14] is played on a 70-by-35-foot Dymaxion map.[15]

In 2013, to commemorate the 70th anniversary of the publication of the Dymaxion map in Life magazine, the Buckminster Fuller Institute announced the "Dymax Redux", a competition for graphic designers and visual artists to re-imagine the Dymaxion map.[16][17] The competition received over 300 entries from 42 countries.[16]

In 2019, Daniel "daan" Strebe used mathematical work on conformal projections by Oscar S. Adams and L. P. Lee to create a conformal version of the Dymaxion projection.[18] In 2020, the Build the Earth project used Strebe's work to create a map projection for their work known as the Modified Airocean. This map projection provides an extremely low amount of distortion of both shapes and sizes on land, at the cost of heavily distorting the oceans. Unlike the Dymaxion, Modified Airocean is not intended to be unfolded into a 3D object like an icosahedron, and has its continents placed such that it looks somewhat similar to an equirectangular projection.[19]

 
 

Comparison of the Fuller projection and Strebe's Dymaxion-like
conformal projection with Tissot's indicatrices at 30° intervals

See also edit

References edit

  1. ^ "Life Presents R. Buckminster Fuller's Dymaxion World". LIFE. 1 March 1943. pp. 41–55.
  2. ^ U.S. patent 2,393,676
  3. ^ Fuller, Ideas and Integrities (1969 ed., p. 139).
  4. ^ Gray, Robert W. (1994-01-01). "Fuller's Dymaxion Map". Cartography and Geographic Information Systems. 21 (4): 243–246. doi:10.1559/152304094782540628 (inactive 31 January 2024). ISSN 1050-9844.{{cite journal}}: CS1 maint: DOI inactive as of January 2024 (link)
  5. ^ Gray, Robert W. (1995-10-01). "Exact Transformation Equations for Fuller's World Map". Cartographica: The International Journal for Geographic Information and Geovisualization. 32 (3): 17–25. doi:10.3138/1677-3273-Q862-1885. ISSN 0317-7173.
  6. ^ Crider, John E. (2008-03-01). "Exact Equations for Fuller's Map Projection and Inverse". Cartographica: The International Journal for Geographic Information and Geovisualization. 43 (1): 67–72. doi:10.3138/carto.43.1.67. ISSN 0317-7173.
  7. ^ "Dymaxion Map Transformations - Technical White Paper", Kitrick, Christopher, 2018
  8. ^ "Fuller—ArcGIS Pro | Documentation".
  9. ^ Fuller, Intuition (1972).
  10. ^ "Frequently Asked Questions About The Fuller Projection", Buckminster Fuller Institute, 1992, accessed 2010-07-28
  11. ^ "Kulturelles Erbe Köln: Johns, Jasper, Map (Weltkarte)". www.kulturelles-erbe-koeln.de. Retrieved 2017-01-18.
  12. ^ "Ausstellung "Ludwig goes Pop"".
  13. ^ Richards, Allen (May–June 1971). "R. Buckminster Fuller: Designer of the Geodesic Dome and the World Game". Mother Earth News. Retrieved 19 January 2014.
  14. ^ Aigner, Hal (November–December 1970). "Sustaining Planet Earth: Researching World Resources". Mother Earth News. Retrieved 19 January 2014.
  15. ^ Perry, Tony (October 2, 1995). "This Game Anything but Child's Play : Buckminster Fuller's creation aims to fight the real enemies of mankind: starvation, disease and illiteracy". The Los Angeles Times. Retrieved 19 January 2014.
  16. ^ a b . The Buckminster Fuller Institute. Archived from the original on 2 February 2014. Retrieved 21 January 2014.
  17. ^ Campbell-Dollaghan, Kelsey (July 22, 2013). "7 Brilliant Reinventions of Buckminster Fuller's Dymaxion Map". Gizmodo. Retrieved 21 January 2014.
  18. ^ Strebe, Daniel. "Directory of Map Projections: dymaxion-like conformal". Mapthematics. Mapthematics LLC. Retrieved 2022-06-19.
  19. ^ Archived at Ghostarchive and the : We are now ready to Build The Earth, 1:1 scale in Minecraft, retrieved 2021-04-01

External links edit

 
Wikimedia Commons has media related to Fuller projection.
  • Fuller Map homepage
  • Icosahedron and Fuller maps
  • Dynamically generated maps based on the Dymaxion projection

January 01, 1970
dymaxion, fuller, projection, world, onto, surface, icosahedron, which, unfolded, flattened, dimensions, flat, heavily, interrupted, order, preserve, shapes, sizes, world, dymaxion, projection, with, graticuledymaxion, projection, with, tissot, indicatrix, def. The Dymaxion map or Fuller map is a projection of a world map onto the surface of an icosahedron which can be unfolded and flattened to two dimensions The flat map is heavily interrupted in order to preserve shapes and sizes The world on a Dymaxion projection with 15 graticuleDymaxion projection with Tissot s indicatrix of deformationAn icosahedron the shape the world map is projected onto before unfolding source source source The world flattens to a Dymaxion map as it unfolds into an icosahedron net with nearly contiguous land masses This icosahedral net shows connected oceans surrounding Antarctica Example of use illustrating early human migrations according to mitochondrial population genetics numbers are millennia before present Dymaxion map of the world with the 30 largest countries and territories by total area roughly to scale The projection was invented by Buckminster Fuller The March 1 1943 edition of Life magazine included a photographic essay titled Life Presents R Buckminster Fuller s Dymaxion World The article included several examples of its use together with a pull out section that could be assembled as a three dimensional approximation of a globe or laid out as a flat map with which the world may be fitted together and rearranged to illuminate special aspects of its geography 1 Fuller applied for a patent in the United States in February 1944 showing a projection onto a cuboctahedron which he called dymaxion The patent was issued in January 1946 2 In 1954 Fuller and cartographer Shoji Sadao produced the Airocean World Map a version of the Dymaxion map that used a modified but mostly regular icosahedron as the base for the projection The version most commonly referred to today it depicts Earth s continents as one island or nearly contiguous land masses The Dymaxion projection is intended only for representations of the entire globe It is not a gnomonic projection whereby global data expands from the center point of a tangent facet outward to the edges Instead each triangle edge of the Dymaxion map matches the scale of a partial great circle on a corresponding globe and other points within each facet shrink toward its middle rather than enlarging to the peripheries 3 Fuller s 1980 version of the Dymaxion map was the first definition and use of a mathematical transformation process to make the map 4 5 6 7 It is a polyhedral map projection The name Dymaxion was applied by Fuller to several of his inventions Contents 1 Properties 2 Impact 3 See also 4 References 5 External linksProperties editThough neither conformal nor equal area 8 Fuller claimed that his map had several advantages over other projections for world maps It has less distortion of relative size of areas most notably when compared to the Mercator projection and less distortion of shapes of areas notably when compared to the Gall Peters projection Other compromise projections attempt a similar trade off More unusually the Dymaxion map does not have any right way up Fuller argued that in the universe there is no up and down or north and south only in and out 9 Gravitational forces of the stars and planets created in meaning towards the gravitational center and out meaning away from the gravitational center He attributed the north up superior south down inferior presentation of most other world maps to cultural bias Fuller intended the map to be unfolded in different ways to emphasize different aspects of the world 10 Peeling the triangular faces of the icosahedron apart in one way results in an icosahedral net that shows an almost contiguous land mass comprising all of Earth s continents not groups of continents divided by oceans Peeling the solid apart in a different way presents a view of the world dominated by connected oceans surrounded by land Showing the continents as one island earth also helped Fuller explain in his book Critical Path the journeys of early seafaring people who were in effect using prevailing winds to circumnavigate this world island However the Dymaxion map can also prove difficult to use It is for example confusing to describe the four cardinal directions and locate geographic coordinates The awkward shape of the map may be counterintuitive to most people trying to use it For example the shortest route from Africa to South America is not obvious Depending on how the map is projected land masses and oceans are often divided into several pieces Impact editA 1967 Jasper Johns painting Map Based on Buckminster Fuller s Dymaxion Airocean World depicting a Dymaxion map hangs in the permanent collection of the Museum Ludwig in Cologne 11 12 The World Game a collaborative simulation game in which players attempt to solve world problems 13 14 is played on a 70 by 35 foot Dymaxion map 15 In 2013 to commemorate the 70th anniversary of the publication of the Dymaxion map in Life magazine the Buckminster Fuller Institute announced the Dymax Redux a competition for graphic designers and visual artists to re imagine the Dymaxion map 16 17 The competition received over 300 entries from 42 countries 16 In 2019 Daniel daan Strebe used mathematical work on conformal projections by Oscar S Adams and L P Lee to create a conformal version of the Dymaxion projection 18 In 2020 the Build the Earth project used Strebe s work to create a map projection for their work known as the Modified Airocean This map projection provides an extremely low amount of distortion of both shapes and sizes on land at the cost of heavily distorting the oceans Unlike the Dymaxion Modified Airocean is not intended to be unfolded into a 3D object like an icosahedron and has its continents placed such that it looks somewhat similar to an equirectangular projection 19 nbsp Fuller projection nbsp Dymaxion like conformal projection Comparison of the Fuller projection and Strebe s Dymaxion like conformal projection with Tissot s indicatrices at 30 intervalsSee also editList of map projections Authagraph projection inspired by Fuller 1999 Peirce quincuncial projection 1879 Polyhedral map projection earliest known is by Leonardo da Vinci 1514References edit Life Presents R Buckminster Fuller s Dymaxion World LIFE 1 March 1943 pp 41 55 U S patent 2 393 676 Fuller Ideas and Integrities 1969 ed p 139 Gray Robert W 1994 01 01 Fuller s Dymaxion Map Cartography and Geographic Information Systems 21 4 243 246 doi 10 1559 152304094782540628 inactive 31 January 2024 ISSN 1050 9844 a href Template Cite journal html title Template Cite journal cite journal a CS1 maint DOI inactive as of January 2024 link Gray Robert W 1995 10 01 Exact Transformation Equations for Fuller s World Map Cartographica The International Journal for Geographic Information and Geovisualization 32 3 17 25 doi 10 3138 1677 3273 Q862 1885 ISSN 0317 7173 Crider John E 2008 03 01 Exact Equations for Fuller s Map Projection and Inverse Cartographica The International Journal for Geographic Information and Geovisualization 43 1 67 72 doi 10 3138 carto 43 1 67 ISSN 0317 7173 Dymaxion Map Transformations Technical White Paper Kitrick Christopher 2018 Fuller ArcGIS Pro Documentation Fuller Intuition 1972 Frequently Asked Questions About The Fuller Projection Buckminster Fuller Institute 1992 accessed 2010 07 28 Kulturelles Erbe Koln Johns Jasper Map Weltkarte www kulturelles erbe koeln de Retrieved 2017 01 18 Ausstellung Ludwig goes Pop Richards Allen May June 1971 R Buckminster Fuller Designer of the Geodesic Dome and the World Game Mother Earth News Retrieved 19 January 2014 Aigner Hal November December 1970 Sustaining Planet Earth Researching World Resources Mother Earth News Retrieved 19 January 2014 Perry Tony October 2 1995 This Game Anything but Child s Play Buckminster Fuller s creation aims to fight the real enemies of mankind starvation disease and illiteracy The Los Angeles Times Retrieved 19 January 2014 a b DYMAX REDUX Winner The Buckminster Fuller Institute Archived from the original on 2 February 2014 Retrieved 21 January 2014 Campbell Dollaghan Kelsey July 22 2013 7 Brilliant Reinventions of Buckminster Fuller s Dymaxion Map Gizmodo Retrieved 21 January 2014 Strebe Daniel Directory of Map Projections dymaxion like conformal Mapthematics Mapthematics LLC Retrieved 2022 06 19 Archived at Ghostarchive and the Wayback Machine We are now ready to Build The Earth 1 1 scale in Minecraft retrieved 2021 04 01External links edit nbsp Wikimedia Commons has media related to Fuller projection Fuller Map homepage Dymaxion Project Animation Icosahedron and Fuller maps Dynamically generated maps based on the Dymaxion projection Retrieved from https en wikipedia org w index php title Dymaxion map amp oldid 1204299490, wikipedia, wiki, book, books, library,

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