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         Heawood Percy:     more detail
  1. Hochschullehrer (Durham): John Frederick Dewey, David Heywood Anderson, Fritz London, David M. Knight, Percy Heawood, William Young Sellar (German Edition)
  2. Vice-Chancellors and Wardens of Durham University: Kenneth Calman, Derman Christopherson, Percy John Heawood, Chris Higgins

81. A NEW PROOF OF THE FOUR-COLOR THEOREM Robin Thomas School Of
Proof refuted by heawood in 1890Kempes ideas used in the ultimate solution16Percy heawoodRefuted Kempes proof
http://www.math.gatech.edu/~thomas/SLIDE/fcsl.pdf

82. Vierkleurenstelling - Wikipedia NL
Gedurende 10 jaar stond de vierkleurenstelling bekend als bewezen, totdatPercy John heawood in 1890 een fout in Kempes bewijs vond.
http://nl.wikipedia.org/wiki/Vierkleurenstelling
Vierkleurenstelling
De vierkleurenstelling is de stelling in de wiskunde dat het mogelijk is elke willekeurige landkaart waarin de landen elk een geheel vormen (dus zonder exclaves ), met behulp van slechts vier kleuren op een dusdanige wijze in te kleuren dat geen twee aangrenzende landen dezelfde kleur krijgen. Twee landen gelden hierbij als aangrenzend als ze een stuk grens gemeen hebben, niet als ze slechts met een punt aan elkaar verbonden zijn. In meer wiskundige termen kan de vierkleurenstelling beschreven worden in de terminologie van de grafentheorie : Van elke vlakke graaf kunnen de knopen op een dusdanige wijze in vier groepen worden verdeeld, dat geen enkele zijde twee knopen van dezelfde groep verbindt. De stelling werd geponeerd in door Francis Guthrie . Enige tijd stond het open als probleem, maar in publiceerde Alfred Bray Kempe een bewijs. Gedurende 10 jaar stond de vierkleurenstelling bekend als bewezen, totdat Percy John Heawood in een fout in Kempes bewijs vond. Het gat kon niet gerepareerd worden; wel gebruikte Heawood Kempes bewijs om aan te tonen dat 5 kleuren voldoende waren, en hij bewees ook diverse andere aan de vierkleurenstelling verwante stellingen. Pas in werd een nieuw bewijs gevonden, door

83. Problema Dels Quatre Colors
La demostració es donà per bona durant 11 anys fins que el 1890, percy John Heawoodféu notar un error en l’argumentació de Kempe i, a més, mostrà que l
http://www.iec.es/institucio/societats/SCMatematiques/AMM/web-posters/pag_4color
Nota sobre el teorema dels quatre colors
Guthriea capensis i Erica Guthriei En les coloracions a què fa referència el problema de Gurthrie, regions no frontereres es poden acolorir amb el mateix color i regions que tenen un únic punt en comú també. Amb aquestes condicions, els mapes de les figures 1(a) i 1(b) es poden acolorir amb només quatre colors, com mostren les figures 1(b) i 2 (b). A més, aquests són exemples de mapes que no es poden acolorir amb menys de quatre colors. El que resulta sorprenent és que, com afirmava Guthrie, per complicat que sigui un mapa es pugui pintar amb només quatre colors. El problema consistia en demostrar que quatre colors són suficients per a qualsevol mapa o bé en trobar-ne un que en requereixi cinc o més. La major part de demostracions errònies es basen en el convenciment que el nombre mínim de colors que cal per pintar un mapa és el màxim nombre de regions dos a dos adjacents. Després es prova que en cap mapa no hi pot haver cinc regions tals que cadascuna sigui adjacent a les altres quatre, un resultat que ja era conegut per De Morgan. La conclusió és immediata: quatre colors són suficients per a qualsevol mapa. Malauradament, la hipòtesi de partida és falsa, com prova el mapa de la figura 3. En aquest mapa el nombre màxim de regions mútuament adjacents és tres, però requereix quatre colors, tres per a les regions de la corona i un altre per a la central.
Bibliografia Kenneth Appel and Wolfgang Haken: La solución del problema del mapa de cuatro colores

84. MMS Online Graph Theory Course Introduction
ten years. However, in 1890, another British mathematician, percy JohnHeawood, found a mistake in Kempe s work. The problem remained
http://www.math.lsa.umich.edu/mmss/coursesONLINE/graph/
Graph Theory and Enumeration
Course designed by Dale Winter
The goals of this project are, firstly, to acquaint you with some of the ideas and principles involved in the mathematical study of counting and combinatorial graphs, and secondly, to provide a starting point for mathematical explorations of your own.
The theory of graphs started in a paper published in 1736 by the Swiss mathematician Leonhard Euler. The idea in Euler's paper, which has blossomed into graph theory, grew out of a now popular problem known as the "Seven Bridges of Königsberg." The problem goes something like this:
It was said that people spent their Sundays walking around, trying to find a starting point so that they could walk about the city, cross each bridge exactly once, and then return to their starting point. Can you find a starting point, and a path around the city that allow you to do this?
Another famous problem that we will develop tools to help us with is the "Four Color Problem."

85. Kamil4
67Edward heawood, A History of Geographical Discoveries in the Sixteenth and SeePercy G Adams, Travellers and Travel Liars 1600-1800 (Berkeley University
http://members.tripod.com/~warlight/KAMIL_4.html
var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded"
The Origins of the Travelogue and its Role in Establishing the Twentieth Century Picture of Turkey As far as the representation of Turkey, its people and culture is concerned, another literary genre to be dealt with in this investigation is travel-writing since 'an examination of the varied texts produced by travellers shows how prejudices, stereotypes and negative perceptions of other cultures can be handed down through generations' ( Comparative Literature , 99). In association with the idea of representing one particular culture, travel writing is considered by various scholars such as Sara Mills, Mary Louise Pratt and Susan Bassnett, to be a part of the process of manipulation which affects and conditions people's attitudes to other cultures in which 'travel writers constantly position themselves in relation to their point of origin in a culture and the context they are describing' ( ). Discussing the significance of travel accounts Bernard Lewis has made a similar conclusion in his "Some English Travellers in the East" where he states, despite some exceptions, that 'all travellers' tales have a not unimportant place in history, at least in that part of it which is concerned with the formation and projection of images' ( The literature of travel has evolved through the centuries. Early examples of travel writing usually appeared in the form of guidebooks and itineraries such as that of Pausanias, who travelled the Mediterranean countries as well as the Nile and the Dead Sea, as far back as the second century AD (

86. History Of Mathematics: Chronology Of Mathematicians
Note there are also a chronological lists of mathematical works and mathematics for China, and chronological lists of mathematicians for the Arabic sphere, Europe, Greece, India, and Japan. Table of
http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html
Chronological List of Mathematicians
Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan
Table of Contents
1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below
List of Mathematicians
    1700 B.C.E.
  • Ahmes (c. 1650 B.C.E.) *MT
    700 B.C.E.
  • Baudhayana (c. 700)
    600 B.C.E.
  • Thales of Miletus (c. 630-c 550) *MT
  • Apastamba (c. 600)
  • Anaximander of Miletus (c. 610-c. 547) *SB
  • Pythagoras of Samos (c. 570-c. 490) *SB *MT
  • Anaximenes of Miletus (fl. 546) *SB
  • Cleostratus of Tenedos (c. 520)
    500 B.C.E.
  • Katyayana (c. 500)
  • Nabu-rimanni (c. 490)
  • Kidinu (c. 480)
  • Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT
  • Zeno of Elea (c. 490-c. 430) *MT
  • Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT
  • Oenopides of Chios (c. 450?) *SB
  • Leucippus (c. 450) *SB *MT
  • Hippocrates of Chios (fl. c. 440) *SB
  • Meton (c. 430) *SB

87. ËÄÉ«¶¨Àí
The summary for this Chinese (Simplified) page contains characters that cannot be correctly displayed in this language/character set.
http://www.2003.com.cn/editor/pupil/200310241595.htm
http://www.2003.com.cn 2003-10-27
»°ËµÔÚ1852Ä꣬ÓÐһλû½Ð¸¥ÀÊÎ÷˹£®¹ÅÌØÀFrancis Guthrie£©µÄ´óѧÉú£¬Ëû·¢ÏÖ¿ÕŵØͼÉϵĹú¼Ò×ÜÊÇ¿ÉÒÔÓËÄÖÖÑÕÉ«À´×ÅÉ«£¬Ê¹ÏàÁÚ¹ú¼ÒµÄÑÕÉ«¶¼²»Ïàͬ¡£µ±ËûÓÐÕâÑùµÄ·¢ÏÖʱ£¬±ãÁ¢¼´ÏòËû¶ÁÊýѧµÄ¸ç¸ç·ÑÌØÀï¿Ë£®¹ÅÌØÀFrederick Guthrie£©Çë½ÌÕâ¸öÎÊÌâµÄÖ¤÷·½·¨£¬µ«·ÑÌØÀï¿ËÈ´»Ø´ð²»µ½¡£·ÑÌØÀï¿ËÒò¶øÏòËûµÄÀÏʦµÂ£®Ä¦¸ù£¨Augustus de Morgan£©Çë½Ì£¬¿ÉϧµÂ£®Ä¦¸ùÒ²ÎÞ·¨Åж¨Õâ¸ö²ÂÏëµÄÕæÈ·ÐÔ¡£¼°ºóµÂ£®Ä¦¸ù±ãÖº¯ËûÔÚÈýһѧԺµÄºÓѹþܶ٣¨Hamilton£©£¬ËûÏàÐŹþܶٿÉÒÔ¸øËû´ð°¸£¬ÔõÁÏÎÊÌâÈ´²»±»¹þܶÙ×¢Òâµ½¡£ 1878Ä꣬Êýѧ¼Ò¿­Àû£¨Cayley£©ÔÚÂ׶ØÊýѧѧ»á¼°»Ê¼ÒµØÀíѧ»áÌá³öÁËÕâ¸öËÄÉ«²ÂÏ룬ËÄÉ«²ÂÏë²Å¿ªÊ¼ÒýÆð¹ã·ºµÄ¹Ø×¢¡£µ«×Ô´ËÖ®ºó£¬¸÷¹úËùÓÐÊýѧÖÐÐĺÍÈ«ÊÀ½çËùÓÐÖ÷ÒªÊýѧÔÓÖ¾¶¼²»¶ÏÊÕµ½ËÄÉ«²ÂÏëµÄ´íÎóÖ¤÷¡£ÆäÖÐÂÉʦ³öÉíµÄ¿ÏÆÕ£¨Alfred Bray Kempe£©ÔÚ1879Äê·¢±íÁËÓйØËÄÉ«²ÂÏëµÄÖ¤÷£¬²¢ÔÚ1880Äê·¢±íµÚ¶þƪµÄÂÛÎÄ¡£×î³õ£¬¿­Àû¼°ÆäËüÊýѧ¼ÒÒ²·¢ÏÖ²»µ½ÓйØÂÛÖ¤µÄÆÆÕÀ£¬Ö±ÖÁ1890Ä꣬ÄêÇáÊýѧ¼ÒÏ£ÎéµÂ£¨Percy John Heawood£©·¢ÏÖÁË¿ÏÆյĩ¶´£¬²¢°Ñ´íÎ󱨸æ¸øÂ׶ØÊýѧѧ»á£¬¶øËûÈ´ÈÏΪ×Ô¼º²»ÄÜ°ÑÕâЩ´íÎóÐÞÕý¹ýÀ´¡£ÆäʵÔÚ1880Ä꣬¿ÏÆյĵڶþƪÂÛÎÄÒ²ÎüÒýµ½Áíһλ×ÔÈ»ÕÜѧµÄѧÕß̨ÌØ£¨Peter Guthrie Tait£©£¬ËûÒ²Ôø·¢±íÁËһЩÓйØËÄÉ«²ÂÏëµÄÂÛÎÄ£¬µ±ÖÐÒ²²»·¦ÐµÄÒâÄ¿ÉϧҲÓв»Éٵĩ¶´£¬»»¾ä»°Ëµ£¬ËÄÉ«²ÂÏëÈÔδ¿É±»Ö¤÷¡£

88. ¥|¦â©w²z
The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set.
http://www.i-mikekong.net/Maths/Problems/4_colour01.html
¼w¡D¼¯®Ú Augustus de Morgan ¡^½Ð±Ð¡A¥i±¤ ¼w¡D¼¯®Ú ¤]µLªk§P©w³o­Ó²q·Qªº¯u½T©Ê¡C¤Î«á ¼w¡D¼¯®Ú «¢±K¹y Hamilton ¡^¡A¥L¬Û«H «¢±K¹y ¥i¥Hµ¹¥Lµª®×¡A«ç®Æ°ÝD«o¤£³Q«¢±K¹yª`·N¨ì¡C ¼w¡D¼¯®Ú ¡@¡@1878¦~¡A¼Æ¾Ç®a ³Í§Q Cayley ³Í§Q ¤U¤@³¹
°Ñ¦Ò®Ñ¥Ø¡G §õ¾Ç¼ÆµÛ¡A¡m¼Æ¾Ç©M¼Æ¾Ç®aªº¬G¨Æ¡@²Ä¤@¶°¡n¡A¤E³¹¥Xª©ªÀ¡A¥xÆW¡A1993¡C

89. 4»ö ¹®Á¦
The summary for this Korean page contains characters that cannot be correctly displayed in this language/character set.
http://mathman.pe.kr/math/color4.htm
  • - Keith DevlinÁöÀ½ / Çã¹Î.¿ÀÇý¿µ ¿Å±è. °æ¹®»ç.
1852³â 10¿ù, ¿µ±¹ ·±´ø¿¡ ÀÖ´Â À¯´Ï¹ö½Æ¼ ´ëÇÐ(University College)ÀÇ ´ëÇпø»ý ÇÁ·£½½º ±¸Æ®¸®¿¡(Francis Guthrie)´Â ¿µ±¹ Áöµµ¸¦ »öÄ¥ÇØ ³ª°¡´Ù°¡
±¸Æ®¸®¿¡´Â ·±´ø´ëÇÐÀÇ ÇлýÀ̾ú´ø ³²µ¿»ý ÇÁ·¹´õ¸¯ÇÑÅ× ¹°¾ú°í, ÇÁ·¹´õ¸¯Àº ´Ù½ ½º½ÂÀÎ ¸ð¸£°£(Augustus De Morgan)¿¡°Ô ¹°¾ú´Ù. ¸ð¸£°£Àº ¶Ç ¾ÆÀÏ·£µåÀÇ ¼öÇÐÀÚÀÌÀÚ À§´ëÇÑ ¹°¸®ÇÐÀÚ¿´´ø ÇعÐÅÏ(William Rowan Hamilton)¿¡°Ô ÆíÁö¸¦ ½è´Ù. ÇعÐÅϵµ ´Ù¼¸ Á¾·ùÀÇ »öÀÌ ÇÊ¿äÇÑ µµÇüÀ» £Áö ¸øÇßÀ¸¸ç, ±×·± µµÇüÀÌ Á¸ÀçÇÏÁö ¾Ê´Â´Ù´Â °ÍÀ» ¼öÇÐÀûÀ¸·Î Áõ¸íÇÒ ¼öµµ ¾ø¾ú´Ù.
±× µÚ ÀÌ ¹®Á¦´Â ºü¸¥ ¼Óµµ·Î À¯·´¿¡ ÀüÆÄµÇ¾î ¿©·¯ »ç¶÷µéÀÇ µµÀüÀ» ¹Þ¾ÒÁö¸¸, ³»·Î¶óÇÏ´Â ¼öÇÐÀڵ鵵 Áõ¸íÇÏÁö ¸øÇß°í, 1878³â ÄÉÀϸ®(F.Cayley)¿¡ ÀÇÇØ °ø½ÄÀûÀ¸·Î Á¦±âµÇ¾ú´Ù.
4»ö¹®Á¦(four color problem)·Î ºÒ¸®´Â ÀÌ ¹®Á¦´Â 1879³â ¿µ±¹ÀÇ ÄÍÆä(Alfred Bray Kempe)¿¡ ÀÇÇØ Ç®·È´Ù. ±×·¸°Ô ¾Ë°í ÀÖ¾ú´Ù.
±×·¯´Ù°¡ 1890³â, ´õ·³ ´ëÇÐÀÇ °­»ç¿´´ø Á¸ È÷¿ìµå(Percy John Heawood)´Â ÄÍÆä°¡ ÇØ°áÇÑ °ÍÀ¸·Î ¾Ë·ÁÁø ³í¹®¿¡¼­ ¿À·ù¸¦ ¹ß°ßÇß°í, À̸¦ ¼öÁ¤ÇÏ¿© ´Ù¼¸ Á¾·ùÀÇ »öÀ¸·Î´Â ¸ðµç Áöµµ¸¦ Ä¥ÇÒ ¼ö ÀÖ´Ù´Â °á·ÐÀ» ³»·È´Ù.
ÀÌ·± ¿¬±¸°úÁ¤¿¡¼­ À§»ó¼öÇÐ(topology)¶ó´Â »õ·Î¿î ºÐ¾ßÀÇ ¼öÇÐÀ» Å©°Ô ¹ßÀü½Ä×´Ù.

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