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Что (кто) такое four colour map theorem - определение
STATEMENT IN MATHEMATICS
Four-Color Theorem; Four-color theorem; Four-colour theorem; Four colour problem; Four color problem; Four-color conjecture; Four Color Theory; Map-coloring problem; Four-Colour Map Problem; Four color map problem; Four-color problem; 4 color theorem; Four Color Theorem; 4CT; Four Colour Theorem; Four-colour problem; Four color map theorem; 4 colour map problem; Four-colour Theorem; Four-Colour Theorem; Four-color map theorem; 4-color conjecture; Four Color Conjecture; 4 color problem; 4-colors theorem; The Four-Color map Theorem; Map color problem; Proof of the 4 color theorem; History of the four color theorem; Four color conjecture; Four colour map problem; Four Color Problem; Map coloring problem; 4-color theorem; Seven colour theorem; 4-color problem; Four-Color Maps; Four-color map; Minimum number of map colors; Four colour theorem; 4 colour theorem; Four-colour map; Four-colour map problem; Four-color map problem; 4 color map problem; Four-Color Map Theorem
![Hamilton]], 23 Oct. 1852](https://commons.wikimedia.org/wiki/Special:FilePath/DeMorganFourColour.png?width=200 "Hamilton]], 23 Oct. 1852")
![By joining the single arrows together and the double arrows together, one obtains a [[torus]] with seven mutually touching regions; therefore seven colors are necessary.](https://commons.wikimedia.org/wiki/Special:FilePath/Torus with seven colours.svg?width=200 "By joining the single arrows together and the double arrows together, one obtains a [[torus]] with seven mutually touching regions; therefore seven colors are necessary.")
![A 6-colored [[Klein bottle]]](https://commons.wikimedia.org/wiki/Special:FilePath/Klein_bottle_colouring.svg?width=200 "A 6-colored [[Klein bottle]]")
![Tietze's]] subdivision of a [[Möbius strip]] into six mutually adjacent regions, requiring six colors. The vertices and edges of the subdivision form an embedding of [[Tietze's graph]] onto the strip.](https://commons.wikimedia.org/wiki/Special:FilePath/Tietze_Moebius.svg?width=200 "Tietze's]] subdivision of a [[Möbius strip]] into six mutually adjacent regions, requiring six colors. The vertices and edges of the subdivision form an embedding of [[Tietze's graph]] onto the strip.")
![Interactive [[Szilassi polyhedron]] model with each of 7 faces adjacent to every other – in [{{filepath:Szilassi_polyhedron_3D_model.svg}} the SVG image,] move the mouse to rotate it](https://commons.wikimedia.org/wiki/Special:FilePath/Szilassi polyhedron 3D model.svg?width=200 "Interactive [[Szilassi polyhedron]] model with each of 7 faces adjacent to every other – in [{{filepath:Szilassi_polyhedron_3D_model.svg}} the SVG image,] move the mouse to rotate it")
![[[Proof without words]] that the number of colours needed is unbounded in three or more dimensions](https://commons.wikimedia.org/wiki/Special:FilePath/visual_proof_mutually_touching_solids.svg?width=200 "[[Proof without words]] that the number of colours needed is unbounded in three or more dimensions")
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four colour map theorem
<mathematics, application> (Or "four colour theorem") The
theorem stating that if the plane is divided into connected
regions which are to be coloured so that no two adjacent
regions have the same colour (as when colouring countries on a
map of the world), it is never necessary to use more than four
colours.
The proof, due to Appel and Haken, attained notoriety by using
a computer to check tens of thousands of cases and is thus not
humanly checkable, even in principle. Some thought that this
brought the philosophical status of the proof into doubt.
There are now rumours of a simpler proof, not requiring the
use of a computer.
See also chromatic number
(1995-03-25)
four colour theorem
Four color theorem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet.
Five color theorem
THEOREM
Five colour theorem; Five-color map theorem; 5-color theorem; Five-color theorem; Five-colour theorem
The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world, the regions may be colored using no more than five colors in such a way that no two adjacent regions receive the same color.
Karnaugh map
METHOD TO SIMPLIFY BOOLEAN ALGEBRA EXPRESSIONS; REFINEMENT OF EDWARD VEITCH'S 1952 VEITCH DIAGRAM
Karnaugh diagram; Karnaugh table; K-map; Karnaugh Map; K map; Kmap; Karnaugh maps; Veitch diagram; K Map; Minterm table; Marquand diagram; Kv-diagram; K maps; K-maps; Karnaugh diagrams; Karnaugh mapping; Map K; Karnaugh Maps; KV diagram; KVS diagram; K diagram; KV-diagram; KVS-diagram; K-diagram; Karnaugh-Veitch diagram; Karnaugh-Veitch map; Karnaugh chart; Karnaugh board; Karnaugh plan; Marquand chart; Marquand map; Veitch chart; Karnaugh–Veitch diagram; Veitch-Karnaugh map; KV map; Karnaugh-Veitch symmetry map; KVS map; KV-map; KVS-map; Veitch-Karnaugh diagram; Karnaugh-Veitch symmetry diagram; Marquand-Veitch diagram; Marquand–Veitch diagram; K-Map; Veitch–Karnaugh map; V-diagram; V-Diagram; V diagram; V Diagram; Diagram V; Diagram K; Karnaugh map method; Karnaugh–Veitch map; Symmetry diagram; Karnaugh–Veitch symmetry diagram; Marquand mapping; Conventional Karnaugh map; Gray Code map; Reflection map (logic optimization); Overlay K-map; Overlay Karnaugh map; Logic map; American style Karnaugh map; European style Karnaugh map; American-style Karnaugh map; European-style Karnaugh map; 1-variable Karnaugh map; 2-variable Karnaugh map; 3-variable Karnaugh map; 4-variable Karnaugh map; 5-variable Karnaugh map; 6-variable Karnaugh map; 7-variable Karnaugh map; 8-variable Karnaugh map; One-variable Karnaugh map; Two-variable Karnaugh map; Three-variable Karnaugh map; Four-variable Karnaugh map; Five-variable Karnaugh map; Six-variable Karnaugh map; Seven-variable Karnaugh map; Eight-variable Karnaugh map; 1-variable K-map; 2-variable K-map; 3-variable K-map; 4-variable K-map; 5-variable K-map; 6-variable K-map; 7-variable K-map; 8-variable K-map; One-variable K-map; Two-variable K-map; Three-variable K-map; Four-variable K-map; Five-variable K-map; Six-variable K-map; Seven-variable K-map; Eight-variable K-map; 1-input Karnaugh map; 2-input Karnaugh map; 3-input Karnaugh map; 4-input Karnaugh map; 5-input Karnaugh map; 6-input Karnaugh map; 7-input Karnaugh map; 8-input Karnaugh map; One-input Karnaugh map; Two-input Karnaugh map; Three-input Karnaugh map; Four-input Karnaugh map; Five-input Karnaugh map; Six-input Karnaugh map; Seven-input Karnaugh map; Eight-input Karnaugh map; 1-input K-map; 2-input K-map; 3-input K-map; 4-input K-map; 5-input K-map; 6-input K-map; 7-input K-map; 8-input K-map; One-input K-map; Two-input K-map; Three-input K-map; Four-input K-map; Five-input K-map; Six-input K-map; Seven-input K-map; Eight-input K-map; Standard Karnaugh map; Standard K-map; Conventional K-map; K-map plotting; K-map reading; K-map labeling; K-map labelling; Svoboda chart
The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W.
Madaba Map
![Jordan]] and a (nearly-obliterated) lion hunting a gazelle](https://commons.wikimedia.org/wiki/Special:FilePath/Sapsaphas Madaba.jpg?width=200 "Jordan]] and a (nearly-obliterated) lion hunting a gazelle")
6TH-CENTURY MOSAIC MAP OF PALESTINE
Madaba map; Map of Madaba; Madaba mosaic map; Madeba map; Madaba Mosaic Map
The Madaba Map, also known as the Madaba Mosaic Map, is part of a floor mosaic in the early Byzantine church of Saint George in Madaba, Jordan. The Madaba Map depicts part of the Middle East and contains the oldest surviving original cartographic depiction of the Holy Land and especially Jerusalem.
Pictorial map
![Pictorial map of [[Paris]] by [[Claes Jansz. Visscher]]](https://commons.wikimedia.org/wiki/Special:FilePath/Map of Paris by Claes Jansz. Visscher - Harold B. Lee Library.jpg?width=200 "Pictorial map of [[Paris]] by [[Claes Jansz. Visscher]]")
![[[Tampa Bay]] aerial view map by [[Maria Rabinky]], 2008](https://commons.wikimedia.org/wiki/Special:FilePath/Tampa-Bay-aerial-map.png?width=200 "[[Tampa Bay]] aerial view map by [[Maria Rabinky]], 2008")
MAP THAT USES PICTURES TO REPRESENT FEATURES
Pictorial maps; Geopictorial maps; Panoramic maps; Bird's eye view maps; Illustrated maps; Cartoon maps; Panoramic map; Illustrated map; Geopictorial map; Cartoon map; Oblique view map; Perspective maps; Pespective maps; Bird's eye view map; Bird's-eye view maps; Bird's-eye view map; Anthropomorphic maps; Picture map; Picture maps; Perspective map; Pictoral map
Pictorial maps (also known as illustrated maps, panoramic maps, perspective maps, bird’s-eye view maps, and geopictorial maps) depict a given territory with a more artistic rather than technical style. It is a type of map in contrast to road map, atlas, or topographic map.
Lagrange's four-square theorem
THEOREM
Bachet's conjecture; Bachet's theorem; Four-square theorem; Bachet conjecture; Bachet theorem; Lagrange four-square theorem; Four square theorem; Four squares theorem; Sum of four squares; Lagrange's 4-square theorem; 4 square theorem; Pythagorean quintuple
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares. That is, the squares form an additive basis of order four.
MAP
![Map of [[Utrecht]], Netherlands (1695).](https://commons.wikimedia.org/wiki/Special:FilePath/Atlas de Wit 1698-pl044-Utrecht-KB PPN 145205088.jpg?width=200 "Map of [[Utrecht]], Netherlands (1695).")
 (cropped).jpg?width=200 "Mean Annual Temperature map of Ohio from \"Geography of Ohio\" 1923")
![The ''[[Hereford Mappa Mundi]]'', [[Hereford Cathedral]], England, circa 1300, a classic "T-O" map with Jerusalem at the center, east toward the top, Europe the bottom left and Africa on the right](https://commons.wikimedia.org/wiki/Special:FilePath/Hereford-Karte.jpg?width=200 "The ''[[Hereford Mappa Mundi]]'', [[Hereford Cathedral]], England, circa 1300, a classic \"T-O\" map with Jerusalem at the center, east toward the top, Europe the bottom left and Africa on the right")
![In a [[topological map]], like this one showing inventory locations, the distances between locations are not important. Only the layout and connectivity between them matters.](https://commons.wikimedia.org/wiki/Special:FilePath/Inventory Locations Represented as a Map.png?width=200 "In a [[topological map]], like this one showing inventory locations, the distances between locations are not important. Only the layout and connectivity between them matters.")
![CIA World Factbook]]'', 2016](https://commons.wikimedia.org/wiki/Special:FilePath/Map of the world by the US Gov as of 2016.svg?width=200 "CIA World Factbook]]'', 2016")
![Relief map]] of the [[Sierra Nevada]]](https://commons.wikimedia.org/wiki/Special:FilePath/Maps-for-free Sierra Nevada.png?width=200 "Relief map]] of the [[Sierra Nevada]]")
![continental shelves]] and [[oceanic plateau]]s (red), the [[mid-ocean ridge]]s (yellow-green) and the [[abyssal plain]]s (blue to purple)}}](https://commons.wikimedia.org/wiki/Special:FilePath/Mid-ocean ridge system.gif?width=200 "continental shelves]] and [[oceanic plateau]]s (red), the [[mid-ocean ridge]]s (yellow-green) and the [[abyssal plain]]s (blue to purple)}}")
![Celestial map by the cartographer [[Frederik de Wit]], 17th century](https://commons.wikimedia.org/wiki/Special:FilePath/Planisphæri cœleste.jpg?width=200 "Celestial map by the cartographer [[Frederik de Wit]], 17th century")
![''[[Tabula Rogeriana]]'', one of the most advanced [[early world maps]], by [[Muhammad al-Idrisi]], 1154](https://commons.wikimedia.org/wiki/Special:FilePath/Tabula Rogeriana 1929 copy by Konrad Miller.jpg?width=200 "''[[Tabula Rogeriana]]'', one of the most advanced [[early world maps]], by [[Muhammad al-Idrisi]], 1154")
![USGS]] [[digital raster graphic]].](https://commons.wikimedia.org/wiki/Special:FilePath/Topographic map example.png?width=200 "USGS]] [[digital raster graphic]].")
VISUAL REPRESENTATION OF A CONCEPT SPACE; SYMBOLIC DEPICTION EMPHASIZING RELATIONSHIPS BETWEEN ELEMENTS OF SOME SPACE, SUCH AS OBJECTS, REGIONS, OR THEMES
Maps; Physical map; Political Map; Physical Map; Electronic map; Road atlases; Political map; Maps and directions; Physical map (cartography); Anachronous map; Map generator; Online maps of the united states; Map reading; Village mapping; Map orientation; Interactive Map; Map (cartography); Climatic map; Geographic map
1. <protocol> Manufacturing Automation Protocol.
2. Mathematical Analysis without Programming.
(1996-12-01)
Gough Map
.jpg?width=200)
![15th C. map of the British Isles based on [[Ptolemy]]'s 2nd C. map](https://commons.wikimedia.org/wiki/Special:FilePath/Descriptio Prime Tabulae Europae.jpg?width=200 "15th C. map of the British Isles based on [[Ptolemy]]'s 2nd C. map")
![Facsimile of the Gough Map by the [[Ordnance Survey]]. First published in 1870, the red transcriptions of ancient names were added in the 1935 edition}}](https://commons.wikimedia.org/wiki/Special:FilePath/Ordnance Survey reproduction Bodleian map Britain 1325-1350.jpg?width=200 "Facsimile of the Gough Map by the [[Ordnance Survey]]. First published in 1870, the red transcriptions of ancient names were added in the 1935 edition}}")
LATE MEDIEVAL MAP OF THE ISLAND OF GREAT BRITAIN
Gough map; The Bodleian Map; The Bodleian map; The Gough map; The Gough Map; The Gough Map of Great Britain; Gough Map of Great Britain; Bodleian Map
The Gough Map or Bodleian Map is a Late Medieval map of the island of Great Britain. Its precise dates of production and authorship are unknown.
Википедия
Four color theorem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. The proof has gained wide acceptance since then, although some doubters remain.
The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken after many false proofs and counterexamples (unlike the five color theorem, proved in the 1800s, which states that five colors are enough to color a map). To dispel any remaining doubts about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas. In 2005, the theorem was also proved by Georges Gonthier with general-purpose theorem-proving software.
