Full Alphabetical Index Translate this page 1189*) Hausdorff, Felix (345*) Hawking, Stephen (1282*) Haytham, Abu Ali al (2490*)Heath, Thomas (199*) Heaviside, Oliver (1209*) heawood, percy (596*) Hecht http://alas.matf.bg.ac.yu/~mm97106/math/alphalist.htm
Seconde "DEMONSTRATION" De N. Lygeros Translate this page En 1890, percy heawood découvrit une erreur dans la façon dontKempe avait traité les régions pentagonales. Un an plus tard http://www.lygeros.org/0048-Seconde_DEMONSTRATION.html
Extractions: Abstract : We mean to analyse the framework of the theorem by Appel and Haken for the planar maps problem, in order to study how one exploits computer in this proof. I. Introduction : En 1852, un jeune étudiant londonnien, Francis Guthrie, écrivit à son frère Frédéric pour lui soumettre une énigme qu'il avait découvert en essayant de colorier une carte des comtés anglais : "Est-il possible avec seulement quatre couleurs (ou moins) de colorier n'importe quelle carte, de telle façon que deux régions ayant une frontière commune ne soient jamais de la même couleur ?" Ne parvenant pas à résoudre l'énigme, Frédéric Guthrie en parla à son professeur l'éminent mathématien Auguste De Morgan. Le 23 Octobre 1852, dans une lettre adressée au très célèbre William Rowan Hamilton, De Morgan avouait qu'il n'avait pas progressé. Tel sont les premières mentions historiques du problème des quatres couleurs. Hermann Minkowski, personnage dominant des mathématiques du XIXe siècle, dit un jour à ses étudiants que l'unique raison pour laquelle ce problème n'était pas résolu était que seuls des mathématiciens de troisième ordre s'y était attaqués ; et il ajouta : "Je devrais pouvoir le démontrer". Quelque temps plus tard il reconnut tout penaud : "J'ai indisposé le ciel par mon arrogance : ma démonstration est, elle aussi, inexacte". Comme l'ont remarqué Thomas Saaty et Paul Kainen : "L'un des nombreux aspects surprenants de ce problème des quatre couleurs est que les contributions les plus importantes ont été faites par des gens qui croyaient apporter la solution".
Exerpts...Euler This is percy heawood s proof, which he gave shortly after findingthe fallacy in AB.Kempe s supposed proof of the 4color theorem. http://mathforum.org/workshops/sum96/discrete/exce.html
Extractions: > I'm looking for an accessible reference for Euler's proof of the Euler-Descartes formula f - e + v = 2 for >convex polyhedra. Also, as long as I have your attention, does anybody know how to use this formula to >prove that five colors are sufficient to draw a map on the sphere? Reading through "Mathematics and the >Imagination" I came across the statement that the proof of this "rests on" Euler's formula. Supposing the latter, let me describe the way I taught this here only yesterday morning: View the vertices as towns, one of which is called "Rome", the edges as elevated highways (`roads' or `dykes'), and the faces as fields, except that one is called "the Sea", since it is initially full of water.
Re: Torae Torae Torae By John Conway Long long ago, percy heawood proved, except when K = 2, that any map on a surfaceof Euler characteristic K could be colored with at most f(K) colors, where I http://mathforum.org/epigone/geometry-forum/groxpalperm/Pine.SUN.3.91.9901190949
Neue Seite 1 Translate this page Heath, Thomas (1861 - 1940). Heavisde, Oliver (1850 - 1925). heawood, percy(1861 - 1955). Hecht, Daniel (1777 - 1833). Hecke, Erich (1887 - 1947). http://www.mathe-ecke.de/mathematiker.htm
Extractions: Abbe, Ernst (1840 - 1909) Abel, Niels Henrik (5.8.1802 - 6.4.1829) Abraham bar Hiyya (1070 - 1130) Abraham, Max (1875 - 1922) Abu Kamil, Shuja (um 850 - um 930) Abu'l-Wafa al'Buzjani (940 - 998) Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843) Aepinus, Franz Ulrich Theodosius (13.12.1724 - 10.8.1802) Agnesi, Maria (1718 - 1799) Ahlfors, Lars (1907 - 1996) Ahmed ibn Yusuf (835 - 912) Ahmes (um 1680 - um 1620 v. Chr.) Aida Yasuaki (1747 - 1817) Aiken, Howard Hathaway (1900 - 1973) Airy, George Biddell (27.7.1801 - 2.1.1892) Aithoff, David (1854 - 1934) Aitken, Alexander (1895 - 1967) Ajima, Chokuyen (1732 - 1798) Akhiezer, Naum Il'ich (1901 - 1980) al'Battani, Abu Allah (um 850 - 929) al'Biruni, Abu Arrayhan (973 - 1048) al'Chaijami (? - 1123) al'Haitam, Abu Ali (965 - 1039) al'Kashi, Ghiyath (1390 - 1450) al'Khwarizmi, Abu Abd-Allah ibn Musa (um 790 - um 850) Albanese, Giacomo (1890 - 1948) Albert von Sachsen (1316 - 8.7.1390)
Extractions: What is the greatest number of color fields that can be arranged so that each maintains a border with all others? Bernard Frize's Heawood, 1999, a pair of painted sculptures in tire permanent collection of the MAMVP, and Heawood, 2003, the thirteen digital prints that introduce this show of the artist's mostly recent paintings, address this thorny question. The works' namesake, British mathematician Percy John Heawood, labored over this and related problems (which originated in cartography) in the years surrounding the turn of the last century; at one point, exploring three dimensional forms, he determined that no more than eight fields of color can abut one another on the surface of a double torus (a volume shaped, in accidental analogy, exactly like a three-dimensional figure eight). The twin Heawood sculptures are based on this formula. Among Frize's few forays into three dimensions (which include Peintures sur un fil [Paintings on a Thread], 1978-80, long strands of nylon coated with countless layers of paint then sandpapered to produce multicolored bars approximately six and a half feet long and an inch and a half in diameter), these double doughnuts are on examinations frustrating, to say the least: Because they're placed on the floor, one side out of sight, it's impossible to verify if all eight color fields really are contiguous. The later, two-dimensional Heawoods, which are based on computer generated images of the sculptures, necessarily fail to demonstrate what the 3-D originals were designed to prove. That these prints introduce an exhibition entitled "Aplat" (Flat) expresses better than anything the penchant for paradox that has guided Bernard Frize's work from the beginning.
Read This: Four Colors Suffice: How The Map Problem Was Solved However percy John heawood at Durham College published an article in 1890 in theQuarterly Journal of Mathematics pointing out a fundamental error in Kempe s http://www.maa.org/reviews/fourcolors.html
Extractions: by Robin Wilson Robin Wilson can write. Of course, we've known that for a long time, from his many previous works (sometimes coauthored): thirteen books (by my last count) on graph theory and combinatorics; four volumes on Gilbert and Sullivan; four on the history of mathematics; one on mathematical stamps; and now a book telling the story of the solution of the four color problem. In writing it always helps to have a topic that is by its very nature an entertaining tale with a large and colorful cast of characters. In the author's own words, taken from the preface, we are told that this cast includes: "Lewis Carroll, the Bishop of London, a professor of French literature, an April Fool hoaxer, a botanist who loved heather, a mathematician with a passion for golf, a man who set his watch just once a year, a bridegroom who spent his honeymoon colouring maps, and a Californian traffic cop." Now let's take a look at the problem: Can every map be colored with at most four colors in such a way that neighboring countries are colored differently? The author explains, for his nonmathematical audience, that a proof that four colors suffice must show that all maps can be colored with four colors only. Showing that millions or billions of maps can be colored with four colors will not do.
Los Cuatro Colores Translate this page Sin embargo, en 1890 percy heawood señaló que la demostración era incorrectaya su vez demostró que todo mapa se puede colorear con cinco colores. http://www.hemerodigital.unam.mx/ANUIES/ipn/avanpers/sept-99/siglo02/sec_5.html
Extractions: Septiembre-Octubre de 1999 El problema de los cuatro colores plantea que un mapa plano de regiones conexas con bordes simples pueda colorearse usando cuatro colores. El origen de este problema se remonta a 1852 cuando Francis Guthrie observó que le bastaban cuatro colores para colorear el mapa de condados inglés. Se preguntó si esto sería cierto para cualquier mapa y preguntó a su hermano, quien a su vez consultó con su maestro Augustus De Morgan. Más adelante, Guthrie emigró de Inglaterra a Sudáfrica y se interesó en la botánica. Como detalle curioso se tiene que para colorear un mapa cuya superficie es una banda de Möbius se necesitan seis colores. Hemeroteca Virtual ANUIES
Mathenomicon.net : Reference : Four Colour Theorem Society. Then in 1890 percy John heawood published a paper showing thatthe Kempe ``proof was fundamentally flawed. However, heawood http://www.cenius.net/refer/display.php?ArticleID=fourcolourtheorem_ency
American Scientist Online - Map Quest It was considered correct for 11 years, until percy John heawood, a mathematicianand classical scholar at Durham Colleges, discovered its fatal flaw. http://www.americanscientist.org/template/AssetDetail/assetid/21979
Extractions: Home Current Issue Archives Bookshelf ... Subscribe In This Section Reviewed in This Issue Book Reviews by Issue New Books Received Publishers' Directory ... Virtual Bookshelf Archive Site Search Advanced Search Visitor Login Username Password Help with login Forgot your password? Change your username see list of all reviews from this issue: July-August 2003 MATHEMATICS Daniel S. Silver Four Colors Suffice: How the Map Problem Was Solved . Robin Wilson. xiv + 262 pp. Princeton University Press. First published by Penguin Books in 2002. $24.95 Progress in mathematics is inevitable: Given enough time, even the most fearsome problem surrenders to some new attack. The fall of Fermat's Last Theorem to Andrew Wiles in the mid-1990s, after battles spanning three and a half centuries, is an example. A less well-known instance is Kenneth Appel and Wolfgang Haken's conquest in 1976 of the Four-Color Problem, the subject of this lively and captivating book by mathematician Robin Wilson. "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," wrote the English mathematician Augustus De Morgan in 1852 to his Irish friend and colleague Sir William Rowan Hamilton. The "fact" is that only four colors are required to color any map in such a way that adjacent regions receive different colors. The student was Frederick Guthrie, but it was Frederick's older brother, Francis, who first proposed it. Francis decided that it must be true after coloring a map of the counties in England, and he allowed Frederick to submit the challenge to De Morgan. "What do you say?" continued De Morgan in his letter to Hamilton. "The more I think of it the more evident it seems."
Extractions: Algebra Explorations Astronomy Biology Chemistry ... NEXT >> Mathematicians have puzzled over this question for more than a century. The so-called "four-color map problem" gained attention in the 1850's, when a mathematics student in London named Francis Guthrie asked whether it is possible to color any map using four or fewer colors so that regions sharing a common boundary are colored differently. He mentioned this perplexing question to his brother Frederick Guthrie, who in turn mentioned it to his teacher, the famous mathematician Augustus De Morgan. In the years to follow, De Morgan discussed the problem with several other mathematicians who also became intrigued by this seemingly simple problem. In 1879, a British lawyer and amateur mathematician named Alfred Bray Kempe announced that he had proved that no more than four colors would be needed for any map. Eleven years later, however, a mathematician named Percy John Heawood found an error in Hempe's proof. Heawood then proved that any map could be completed with five colors. Finally, in 1976, two math professors at the University of Illinois, Kenneth Appel and Wolfgang Haken, used a computer to help prove that only four colors are necessary to complete any map. They had solved one of the biggest problems in mathematics!
Jorma Kypp ilmestyi jo 1879, mutta tuo Arthur Kempen kuuluisuuta saanut todistus osoitettiinvirheelliseksi yksitoista vuotta myöhemmin 1890 (percy John heawood). http://www.cs.jyu.fi/~jorma/4cc.htm
The 4 Color Map Problem conjecture is true. His argument was considered correct until 1890when percy John heawood discovered a flaw. Work by many people http://www.math.utah.edu/~alfeld/math/4color.html
Extractions: Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah Suppose you have a map. Let's rule out degeneracies where a country has separate parts (like the continental U.S. and Alaska). Suppose you want to color all countries so they are easy to distinguish. In particular you want to color neighboring countries with different colors. How many colors do you need at most? (Two countries are " neighboring" if they share a border segment that consists of more than one point. If sharing one point was enough to be neighbors you could divide a pie into arbitrarily many slices all of which share the center, requiring as many colors as there are slices). In 1852, Francis Guthrie wrote to his brother Frederick saying it seemed that four colors were always sufficient, did Frederick know a proof. Frederick asked his advisor Augustus De Morgan. Morgan did not know either. In 1878 the mathematician Arthur Cayley presented the problem to the London Mathematical Society. Less than a year later Alfred Bray Kempe published a paper purporting to show that the conjecture is true. His argument was considered correct until 1890 when Percy John Heawood discovered a flaw. Work by many people continued and the conjecture was finally proved true in 1976 by Kenneth Appel and Wolfgang Haken.
Graph Theory Article For Social Measurement In 1890, percy John heawood extended the idea of mapcolouring problemsto consider colourings on surfaces other than the sphere. http://www.math.fau.edu/locke/socialmeasurement/article.htm
Extractions: A graph can be thought of as a representation of a relationship on a given set. For example, the set might be the set of people in some town, and the relationship between two people might be that they share a grandparent. Graph Theory is the study of properties of graphs. In particular, if the graph is known to have one property, what other properties must it possess? Can one find certain features of the graph in a reasonable amount of time? In this article, we mention a few of the more common properties, some theorems relating these properties, and refer to some methods for finding structures within a graph. Glossary
The Origins Of Proof IV: The Philosophy Of Proof Unfortunately, in 1890, 11 years later, percy heawood found an errorin the proof which nobody had spotted despite careful checking. http://plus.maths.org/issue10/features/proof4/
Extractions: Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Issue 10 January 2000 Contents Features Self-similar syncopations In space, do all roads lead to home? Codes, trees and the prefix property The origins of proof IV: The philosophy of proof Career interview Career interview: Sales forecasting Regulars Plus puzzle Pluschat Letters Staffroom A good BETT Book reviews News from January 2000 All the latest news ... poster! January 2000 Features In this final article in our series on Proof, we examine the philosophy of mathematical proof. What precisely is a proof? The answer seems obvious: starting from some
Four Colors Suffice : How The Map Problem Was Solved percy heawood published a paper in which he included a diagram that Kempesmethod could be used on and for which Kempes method failed. http://www.cookingreviews.com/Four_Colors_Suffice_How_the_Map_Problem_Was_Solved
Extractions: This book deserves every star it gets from me! The quality of the writing startled me since afterall it was written by a mathematician. The four color problem was presented in a fascinating manner. Brief histories on the people who worked on the problem were very interesting and added flavor. Also, the book was not dry. It had nice anecdotes and a sense of humor ("humour"-see below). Diagrams and formulas were presented in a very clear concise manner to anyone who has a good geometrical foundation or higher.
BSHM: Gazetteer -- N Can anyone provide more details Newport, Shropshire. percy John heawood (18611955)was born here Biggs, Lloyd Wilson, p. 217. Newton Abbot, Devon. http://www.dcs.warwick.ac.uk/bshm/zingaz/N.html
Extractions: The British Society for the History of Mathematics HOME About BSHM BSHM Council Join BSHM ... Search Main Gazetteer A B C D ... Z Written by David Singmaster (zingmast@sbu.ac.uk ). Links to relevant external websites are being added occasionally to this gazetteer but the BSHM has no control over the availability or contents of these links. Please inform the BSHM Webster (A.Mann@gre.ac.uk) of any broken links. [When the gazetteer was edited for serial publication in the BSHM Newsletter, references were omitted since the bibliography was too substantial to be included. Publication on the web permits references to be included for material now being added to the website, but they are still absent from material originally prepared for the Newsletter - TM, August 2002] Return to the top. Dafydd Nanmor lived in the early 15th Century at Nanmor (probably Nantmor ) on the south side of Mt. Snowdon - he was a poet and "was fond of puzzles, astronomy, and grammar" [Beazley & Howell, p. 153]. Nelson, Lancashire
BSHM: Gazetteer -- Oxford Individuals percy John heawood (18611955) was a student at Exeter College. Heremained at Oxford until 1887 Biggs, Lloyd Wilson, p.217. http://www.dcs.warwick.ac.uk/bshm/zingaz/OxfordPeople.html
Extractions: The British Society for the History of Mathematics HOME About BSHM BSHM Council Join BSHM ... Search Main Gazetteer A B C D ... Z Written by David Singmaster (zingmast@sbu.ac.uk ). Links to relevant external websites are being added occasionally to this gazetteer but the BSHM has no control over the availability or contents of these links. Please inform the BSHM Webster (A.Mann@gre.ac.uk) of any broken links. [When the gazetteer was edited for serial publication in the BSHM Newsletter, references were omitted since the bibliography was too substantial to be included. Publication on the web permits references to be included for material now being added to the website, but they are still absent from material originally prepared for the Newsletter - TM, August 2002] This page contains information about individuals associated with Oxford. Click here to return to the main entry for Oxford , which covers institutions and places. Thomas Allen Aristotle Elias Ashmole Michael Atiyah ... Bertrand Russell John Wellesley Russell - see under Balliol College in the Oxford Institutions section Henry Savile Michael Scot John Sinclair ... Mary Somerville.
Extractions: FREE Zurich Insurance Quote - - - - - Please select product - - - - - Zurich Travel Insurance Zurich YUPPIE Plan Zurich Family Personal Accident Plus Zurich Pension Plus Zurich 5-Year Life Protection Home About Us Contact Us Subscribe ... Sports Tuesday, June 24, 2003 SCIENCE Four colors are enough By Rony V. Diaz A FASCINATING and entertaining book about a famous problem in mathematics was published last month. Its called Four Colors Suffice: How the Map Problem was Solved. The author, Robin Wilson, is a fellow at Keble College, Oxford University. The publisher is Princeton University Press. The four-color conjecture is simplicity itself. It asserts that four colors are enough to mark off any area on a map such that no areas sharing a border are of the same color. Is this true? The conjecture dates back to 1852 when Francis Guthrie, while coloring a map of England, noticed that he needed no more than four colors with no counties having a common border being in the same color. Guthrie told his brother, Frederick, who in turn told Augustus de Morgan, a professor of mathematics.
