Sci.math FAQ: The Four Colour Theorem Subject sci.math FAQ The four colour theorem. 429567. N. Robertson, D. Sanders,P. Seymour, R. Thomas The four colour theorem Preprint, February 1994. http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/fourcolour.html
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Four Colour Map Theorem From FOLDOC four colour theorem . four colour map theorem. mathematics, application (Or four colour theorem ) The theorem stating that if http://csai03.is.noda.sut.ac.jp/foldoc/foldoc.cgi?four colour theorem
Four Colour Map Theorem From FOLDOC four colour theorem . four colour map theorem. mathematics, application (Or four colour theorem ) The theorem stating that if http://www.instantweb.com/D/dictionary/foldoc.cgi?four colour theorem
Sci.math FAQ: The Four Colour Theorem sci.math FAQ The four colour theorem. 21, 1977, pp. 429567. N. Robertson, D. Sanders,P. Seymour, R. Thomas The four colour theorem Preprint, February 1994. http://www.uni-giessen.de/faq/archiv/sci-math-faq.fourcolour/msg00000.html
Four Colour Theorem four colour theorem. Start your search on four colour theorem. Othereducational search engines Ask Jeeves for Kids Britannica http://www.virtualology.com/virtualpubliclibrary/hallofeducation/Mathematics/Fou
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Four Colour Theorem Denis Howe dbh@doc.ic.ac.uk . Previous four colour map theorem NextFourier transform. four colour theorem. four colour map theorem. http://burks.brighton.ac.uk/burks/foldoc/90/44.htm
Four Colour Map Theorem uk . Previous fourcolour glossies Next four colour theorem. fourcolour map theorem. mathematics, application (Or four colour http://burks.brighton.ac.uk/burks/foldoc/89/44.htm
Extractions: The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk Previous: four-colour glossies Next: four colour theorem mathematics application 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
The Four Colour Theorem Question is there an actual equation for the four colour map theorem? i cannotfind it anywhere!! if so can you give a breif description on how it works!! http://mathcentral.uregina.ca/QQ/database/QQ.09.02/rhonda1.html
Extractions: Hi Rhonda, The theorem is just that, a theorem, and it proves that any map in the plane can be coloured properly with just 4 colours. That is not the same as saying that there is an efficient algorithm to 4-colour any planar map; it just assures us that it can actually be done. Thus unless your map is quite small and not too complicated it may be a very difficult task indeed to actually colour it properly with 4-colours. Cheers, Penny
Extractions: This paper is cited in the following contexts: On Local Transformation of Polygons with Visibility.. - Hernando, Houle, Hurtado (Correct) ....the Platonic solids. In recent years, the use of computers has allowed the investigation of structures far more complex than those considered by the ancients. In graph theory, the only proofs yet known of the famous Four Color Theorem have been obtained by means of computer enumeration of cases Also, a general purpose program for computing automorphism groups of graphs and digraphs developed by Brendan McKay, Nauty, has been used to prove a number of graph theoretic results, most notably C. Hernando and F. Hurtado partially supported by CUR Gen. Cat . 1999SGR00356 and MEC DGES SEUID ....
Extractions: Abstract: this paper we focus on the torus and on ostensibly the most dicult case when the graph is a six-regular triangulation; in [28] Thomassen asks for a characterization of the non-4-colorable, 6-regular graphs on the torus. A theorem of Altshuler [4] shows that every 6regular toroidal graph can be represented as a 6-regular shifted rectangular grid on the torus; see Figure 2. A shift of one is the same as an unshifted grid. This allows us to focus rst on 6-regular grids and then to extend our... (Update)
ColourTheory The four colour theorem (or the Four Color Theorem). Mathematicians Nomore so than in the area of the four colour theorem. This http://www.adit.co.uk/html/colourtheory.html
Extractions: RGB and CYMK Colours The Four Colour Theorem (or the Four Color Theorem) Mathematicians and map makers share a lot of common ground. No more so than in the area of the four colour theorem. This theorem simply states that any map in a single plane can be coloured using four-colours in such a way that any regions sharing a common boundary (other than a single point) do not share the same colour. The theorem was first propounded by F Guthrie in 1853. Fallacious proofs have come and gone starting with Kempe in 1879 and Tait an 1880. In 1977 K. Appel and W. Haken used computer assistance to test many different combinations to effectively prove that four colours was all that was required in all instances. Since then, it may be that a mathematical proof has, at last, been arrived at. So, if we know that we can colour any map using just four colours how to we go about it. A little though would indicate that the problem is not straightforward. Simply starting with a random colour and an arbitrary polygon would soon lead to an impasse when the process met an area bounded by more than three other areas yet to be coloured. Kempe is credited with first recording that, when tackling a map of national boundaries, those with three or fewer neighbours presented no problems. His solution was to ignore (temporarily remove from the map) those countries with three or fewer neighbours. This process will immediately simplify the remainder of the map and can be repeated until only countries with three or fewer neighbours remain. The remaining areas can then be coloured. Then the missing countries can be restored in reverse order to their removal and coloured as the process proceeds. This effective procedure is know as Kempe transformations.
Map Colours Colour and Maps. The four colour theorem says that the areas of a mapcan be coloured in using just four colours. Ignore the minimalists http://www.adit.co.uk/html/map_colours.html
Extractions: RGB and CYMK Colours Colour and Maps The four colour theorem says that the areas of a map can be coloured in using just four colours. Ignore the minimalists - colour has an important part to play in communicating information held on a map. Wise colour choice and colour usage can enhance the experience of your map users. The poor use of colour can degrade you map and make it difficult to use. Good colour choice like any design issue seems to demand a little flair and it is difficult to define hard a fast rules. Review other maps you have seen that have a similar purpose to your map. Try and decide where the use of colour has enhanced the objectives and where it has detracted from the map. This may help you decide upon how to apply colour to your specific map. If your map is likely to be photocopied or faxed (perhaps a how to find us map) then this should be taken into account when designing it. A monochrome line drawing might work better than a map with coloured areas and text. Reds and blacks fax well, blues and greens do not. If place and location names or any other form of text are an important attribute of your map then your colour scheme should take this into account. Colour contrasts could become very important to ensure that your text stands out on the relevant background areas.
Maths Thesaurus: Four Colour Theorem Home four colour theorem Any network of points and lines in a plane can be colouredin using no more than four colours, in such a way that no two adjacent http://thesaurus.maths.org/dictionary/map/word/3028
Count On emphasise the changes due to the morphing (A large version of the tiling is downloadableas an Acrobat PDF file as MT7.pdf) The four colour theorem A tiling http://www.mathsyear2000.org/explorer/morphing/13usedownload.shtml
Extractions: There are a number of morphing tilings on the Downloads page . The following are a few suggestions for using them and any you might create yourself to explore patterns in new ways. Morphing patterns are more complex than simply repeating patterns and so offer more possibilities for creativity. Creating tilings can be a slow process if you draw them by hand, although a computer can speed up the process, with the right drawing package. Once you have a set of tiles then you can copy them to build up the tiling. To help you create tilings easily, you can also download a set of True Type fonts which allow you to create tilings in a word-processor. Type in a character and a tile appears. Click here for instructions on how to use these fonts. These pages plus the download files are meant as starting points from which to develop your own ideas. We hope you will find new ways to create new tilings, not just copy the ones here. Analysing the patterns in the tilings Everyone sees something different in morphing tilings. As the eye wanders over them it is possible to see the changes in different ways - sometimes you can focus on a local pattern and sometimes you see a movement over a larger area which is hard to pin down. They are ideal for teaching analytical skills and being able to put discoveries into words. Seeing what is happening is only the first step in showing someone else what you can see.
LinuxGuruz Foldoc Page Affordable Web Hosting. Cheap Web Hosting. Was our site helpfull? Want to make adonation? $. LinuxGuruz Foldoc. four colour theorem . four colour map theorem. http://foldoc.linuxguruz.org/foldoc.php?four colour theorem
Claim Of Proof To Four-Color Theorem The recent announcement by two American computer scientists that they have a proofof the four colour theorem, although they certainly have not published a http://www.lawsofform.org/gsb/nature.html
Extractions: 17 December 1976 Sirs The recent announcement by two American computer scientists that they have a proof of the four colour theorem, although they certainly have not published a proof, coupled with the fact that they are widely reported as saying they believe that no simple or elegant proof of this theorem is possible, prompts me to refer to the work of me and my brother, the late D J Spencer-Brown, on this theorem as early as 1960-1964. As reported in 1969 [ ], we found during this period an extremely elegant way of expressing the four-colour conjecture (as it then was) which, if verified, would lead to a correspondingly elegant proof. As is well known, the difficulty of the foul colour problem stems from the fact that the Heawood formulae [ ], say Hmin, Hmax, giving the minimum and maximum values for the chromatic numbers of surfaces (Sg) of connectivity g, give Hmin = Hmax = [(1/2)(7 + (24g - 23)^(1/2) )] for g > 1
Four Color Theorem the book. The MacTutor History of Mathematics archive at Saint Andrewshas a nice article on the four colour theorem. A summary http://grail.cba.csuohio.edu/~somos/4ct.html
Extractions: Around 1998 Paul Kainen and I worked on an approach to the Four Color Theorem. He is a co-author of a book on this topic reprinted by Dover Publications. AUTHOR Saaty, Thomas L. TITLE The four-color problem : assaults and conquest / Thomas L. Saaty and Paul C. Kainen. PUBLISH INFO New York : Dover Publications, 1986. DESCRIPT'N vi, 217 p. : ill. ; 21 cm. NOTE Includes bibliographical references (p. 197-211) and index. SUBJECTS Four-color problem. LC NO QA612.19 .S2 1986. DEWEY NO 511/.5 19. OCLC # 12975758. ISBN 0486650928 (pbk.) : $6.00. AUTHOR Saaty, Thomas L. TITLE The four-color problem : assaults and conquest / Thomas L. Saaty and Paul C. Kainen. PUBLISHER New York : McGraw-Hill International Book Co., c1977. DESCRIPTION ix, 217 p. : ill. ; 25 cm. NOTES Bibliography: p. 197-211. Includes index. OCLC NO. 3186236. ISBN 0070543828 : $23.00. We take a pair of triangulations of a polygon and four color the vertices such that no two of the same color are connected by an edge of the triangulations. Polygon triangulations are easy to represent using data structures and the topological considerations of planarity are avoided. This turns the problem into a combinatorial one. The planarity reduces to circular order along the polygon and the non-crossing of diagonals. The history of this approach going back to Hassler Whitney and other references to this approach are in the book.
The Four Colour Theorem The four colour theorem. The Four Colour errors. The four colour theoremreturned to being the Four Colour Conjecture in 1890. Percy John http://math.5u.com/The four colour theorem.htm
Extractions: Cheap Web Site Hosting The Four Colour Conjecture first seems to have been made by Francis Guthrie . He was a student at University College London where he studied under De Morgan . After graduating from London he studied law but by this time his brother Frederick Guthrie had become a student of De Morgan . Francis Guthrie showed his brother some results he had been trying to prove about the colouring of maps and asked Frederick to ask De Morgan about them. De Morgan was unable to give an answer but, on 23 October 1852, the same day he was asked the question, he wrote to Hamilton in Dublin. De Morgan wrote:- A student of mine asked me today to give him a reason for a fact which I did not know was a fact - and do not yet. He says that if a figure be anyhow divided and the compartments differently coloured so that figures with any portion of common boundary line are differently coloured - four colours may be wanted, but not more - the following is the case in which four colours are wanted. Query cannot a necessity for five or more be invented. ...... If you retort with some very simple case which makes me out a stupid animal, I think I must do as the Sphynx did.... Hamilton replied on 26 October 1852 (showing the efficiency of both himself and the postal service):- I am not likely to attempt your quaternion of colour very soon.
Bookmarks Four Colors QUESTIONS FAQ. sci.math FAQ The four colour theorem http//www.cs.ruu.nl/wais/html/na-dir/sci-math-faq/fourcolour.html up. http://perso.wanadoo.fr/patrick.davalan/Liens/liens_4colors.html
University Of Wuppertal - Dep. Of Mathematics - Poster imaginary maps. It has taken more than 100 years before a correctproof for the four colour theorem has been found. The proof by http://www.math.uni-wuppertal.de/org/Poster/TextE.htm
Extractions: In 1852, while colouring a map representing the english counties, the british mathematician Francis Guthrie realized that only four colours where necessary to satisfy the criterion that neighbouring counties should have different colours. It turns out that this is true for any (real or imaginary) map. The poster shows such a colouring for the countries of Europe and, in small, for three other imaginary maps. It has taken more than 100 years before a correct proof for the four colour theorem has been found. The proof by Appel and Haken in 1976 has solicited much of a controversial discussion since it heavily relies on computer calculations. These are so extensive that humans cannot verify them "by hand". Consequently, proving the four colour theorem correct also means proving that the program is implemented correctly and that the computer works correctly. Instead of taking Europe and its countries, we could illustrate the four colour theorem with Germany and its regions. This can be found at MathePrisma (in German). There you can also colour some other maps on your own and develop strategies to get the right colouring fast.
