Newsletter Item of the meeting by describing the origins of the problem and presenting the fallacious(but useful) proof by Alfred Kempe and its refutation by percy heawood. http://www.lms.ac.uk/newsletter/0212/articles.html
Extractions: LMS/BSHM JOINT MEETING ON THE FOUR-COLOUR PROBLEM A meeting commemorating the 150th anniversary of the four-colour problem and the 25th anniversary of its published solution took place on 23 October 2002 at University College London, in the attractive Cruciform Lecture Theatre. This event, organised jointly by the London Mathematical Society and the British Society for the History of Mathematics, was the centrepiece of a whole week of commemorative events at six venues with four guest speakers from the US. The afternoon meeting was attended by about 100 people. It opened with a short welcoming speech by Dr June Barrow-Green, Vice-President of the BSHM, who remarked on the appropriateness of time and place of the meeting 150 years to the day of the posing of the problem by a student at University College and thanked the LMS for its support and encouragement to the BSHM over many years. After tea in the North Cloisters, we returned for a short formal LMS meeting chaired by Trevor Stuart, at which several new members signed the LMS membership book. This was followed by two talks on more recent work. Dan Archdeacon (Vermont) gave a lively presentation of the work of Gerhard Ringel, Ted Youngs and others on problems that involve the colouring of maps on general surfaces (both orientable and non-orientable), using the underlying ideas of current and voltage graphs. Finally, Robin Thomas (Atlanta) gave an exciting lecture in which he outlined the more recent solution by Robertson, Sanders, Seymour and himself; although based on the approach of Appel and Haken, it was simpler to understand, and involved only half as many configurations as those given by Appel and Haken. He also outlined some unexpected connections between the four-colour problem and problems from vector algebra, number theory and Lie groups, and concluded by stressing that the four-colour problem is by no means the end of the road there are several unsolved problems that generalize the four-colour problem, to whose solutions Thomas and his co-workers have recently been making exciting progress.
Spektrum Der Wissenschaft Translate this page Eine mit dem Erde-Mond-Problem verwandte Frage hat 1890 der britischeMathematiker percy John heawood (1861 bis 1955) gestellt. http://www.wissenschaft-online.de/abo/spektrum/archiv/1852
Extractions: Hier können Sie Ihre persönlichen Einstellungen verändern. Lassen wir die technischen Probleme der Eroberung des Mondes einmal beiseite. Dann bleibt immer noch ein bedeutendes kartographisches Problem: Wie macht man eine politisch korrekt gefärbte Landkarte von Erde und Mond zusammen? Von Ian Stewart Aus Spektrum der Wissenschaft Mai 1998 , Seite 12, Beitragstyp Mathematische Unterhaltungen Der Name Erde-Mond-Problem ist ein wenig bombastisch für eine Aufgabe, die nichts weiter ist als eine Verallgemeinerung des bekannten Vierfarbenproblems: Irgendwann in der Zukunft haben die Nationen die Erde einschließlich der Weltmeere so unter sich aufgeteilt, daß jeder von ihnen ein zusammenhängendes - nasses, trockenes oder gemischtes - Stück Erdoberfläche gehört. Außerdem hat jede Nation noch einen Teil des Mondes in Besitz genommen. Es ist eine Landkarte von Erde und Mond zusammen nach den üblichen Prinzipien zu färben: Das irdische und das lunare Territorium jedes Landes sollen die gleiche Farbe erhalten, und nirgends sollen zwei aneinandergrenzende Länder mit der gleichen Farbe eingefärbt werden. Wie viele Farben würden in jedem Falle dafür ausreichen, einerlei wie auf beiden Himmelskörpern die Grenzen verlaufen? Dieses Problem, das ich schon im September 1993 in dieser Rubrik beschrieben habe, klingt ziemlich weit hergeholt und künstlich. Ein typisches nutzloses Produkt aus dem Elfenbeinturm der Wissenschaften?
Spektrum Der Wissenschaft Translate this page Nach einem Satz des englischen Mathematikers percy John heawood (1861 bis1955) läßt sich jeder Graph der Dicke 2 mit 12 Farben färben. http://www.wissenschaft-online.de/abo/spektrum/archiv/3935
Extractions: Hier können Sie Ihre persönlichen Einstellungen verändern. Es spotte niemand über die Leute, die fiktive Landkarten von Welten studieren, auf denen es keine Länder gibt. Richtig angewandt, kann deren Wissenschaft sogar echtes Geld einbringen. Von Ian Stewart Aus Spektrum der Wissenschaft Juni 1998 , Seite 10, Beitragstyp Mathematische Unterhaltungen Das Problem, das ich im letzten Monat beschrieben habe, wird wohl kaum in absehbarer Zukunft aktuell werden: korrekte Färbung von Landkarten für Erde, Mond und Mars zusammen. Aber hinter der esoterischen Aufgabenstellung steckt nützliche Mathematik. Wie ich im letzten Monat erklärt habe, nennt man einen Graphen planar, wenn man ihn in der Ebene zeichnen kann, ohne daß sich irgendwelche Kanten kreuzen. Eine Stufe höher stehen Graphen der Dicke 2. Ihre Kanten kann man in zwei Mengen zerlegen, die jede einen planaren Graphen bilden (Bild 2). Ein Graph hat die Dicke 3, wenn man seine Kanten in drei Teilmengen zerlegen kann und muß , so daß jede von ihnen kreuzungsfrei ist, und so weiter. Stellen Sie sich einen Graphen der Dicke 2 als Sandwich vor. Auf die untere Brotscheibe zeichnen wir vielleicht mit Tomatenketchup kreuzungsfrei die Kanten der ersten Menge und auf die obere die Kanten der zweiten Menge, ebenfalls kreuzungsfrei. Die Knoten werden zu vertikalen Linien; denken Sie an Partyspießchen, die durch alle Scheiben gestochen werden. (Sie müssen das Sandwich ja hinterher nicht aufessen.) Ein Graph, für den man d Brotscheiben braucht, hat die Dicke d (Bild 2).
Victorian Photographers List - Birmingham, Warks & Others percy WYNNE,, 174 Broad Street,, Birmingham was EB MOWIL prior to c 1927. heawood,,Welford Place,, Leicester, and at King Richard Rd, Leicester. http://www.hunimex.com/warwick/photogs.html
Extractions: Name Address Location Studios in Birmingham: Nelson Passage (opposite Market Hall) Bull Ring, Birmingham. Edmund S. BAKER Art Studios, 82 Bristol St., Birmingham 154 Bristol St., Birmingham, from about 1896-9 Egeston BAKER, Northlight Studios, 220 Deritend Bridge, Birmingham W. BAKER, Highgate Studios 110 Moseley Road 62 Bordesley, Birmingham W.B. BARBER, 37 Broad St. Birmingham Worcester. BIRCHLEY, 220 High Street, Birmingham - c. 1890 BIRMINGHAM Photograph Studio, 5 Union Passage, Birmingham J. BURTON, Artist, Aston, Birmingham Winifred COOPER, The Studio, 72 Wolverhampton Rd, Birmingham 32. c. 1940's 269 Castle St., Dudley A E DAWSON, 73 Station Road, Kings Heath, Birmingham Ernest DYCHE, 32, Coventry Road, Birmingham Frank EVANS, 14 Trafalgar Road
Extractions: Medieval and Early Modern Aurner, Nellie Slayton. Caxton, Mirrour of Fifteenth-Century Letters: A Study of the Literature of the First English Press . London: P. Allan and Co.; Boston: Houghton Mifflin, 1926. [* Subject heading: early printed books; incunabula *] Avis, Frederick C. "The Growth of London Printing, Publishing, and Bookselling in the Sixteenth Century." Gutenberg-Jahrbuch 1974 , 100-109. [* Subject heading: early printed books; incunabula *] Bennett, H[enry] S[tanley]. "Caxton and His Public." Review of English Studies 19 (1943): 113-119. [* Subject heading: early printed books; incunabula *] Blake, Norman F. William Caxton: A Bibliographical Guide . New York and London: Garland Publishing, 1985. [* Subject heading: early printed books; incunabula *] Carlson, David R. "Woodcut Illustrations of the Canterbury Tales The Library 6th ser. 19 (1997): 25-67. [* Subject heading: early printed books: production; incunabula; book illustration (woodcuts) *] Clark, Peter. "The Ownership of Books in England, 1560-1640: The Example of Some Kentish Townsfolk." In
Extractions: Lets go back to that problem I set you three weeks ago: Place eight more dots on the grid lines so that both these conditions hold: Every horizontal and vertical line contains three dots. The boundary of each of the nine small squares contains three dots. Now, in mathematical terms this seems quite daunting. There are 34 places where a dot could be placed (see below). Thankfully, however, the choice somewhat limits itself. Considering just the grid lines of the puzzle, we need another 14 dots worth (i.e. there need to be 7 dots countable on the horizontal lines, and 7 dots countable on the vertical lines). Because we only have 8 dots to play with, six dots have to be counted twice and the only way of doing this is by placing them on the intersections of the grid. Only two of the new dots can be on any of the square sides (i.e. on A, C, D, F, G, H etc.) For similar reasons, we can assume that no one position will have more than one coin. Given the constraints in the puzzle, we have 17 possible equations (9 for the squares, 4 horizontal lines, 4 vertical lines) to find 34 unknowns. This is too many to calculate, but those unknowns are somewhat limited so if we know that B is definitely a dot, then A, C, D, E, F, G, J and K cannot be.
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: Issue 23: Jan 03 Issue 22: Nov 02 Issue 21: Sep 02 Issue 20: May 02 Issue 19: Mar 02 Issue 18: Jan 02 Issue 17: Nov 01 Issue 16: Sep 01 Issue 15: Jun 01 Issue 14: Mar 01 Issue 13: Jan 01 Issue 12: Sep 00 Issue 11: Jun 00 Issue 10: Jan 00 Issue 9: Sep 99 Issue 8: May 99 Issue 7: Jan 99 Issue 6: Sep 98 Issue 5: May 98 Issue 4: Jan 98 Issue 3: Sep 97 Issue 2: May 97 Issue 1: Jan 97 by Robert Hunt 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 axioms , a proof is a series of logical deductions , reaching the desired conclusion. Every step in a proof can be checked for correctness by examining it to ensure that it is logically sound, and you can tell that you've proved a theorem once and for all by making sure that every step is correct. This might sound simple enough, but one problem is that humans (and even computers) are fallible: what if the person checking a proof for correctness makes a mistake and thinks that a step which is logically incorrect is in fact correct? Obviously somebody else will need to check that the person doing the checking didn't make any mistakes; and somebody will need to check that person, and so on. Eventually you run out of people who could check the proof: and in theory they could
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.
Biblio - Title heawood 1969 Watermarks, Mainly of the 17th and 18th Centuries (Hilversum, 1950R1957 percy 1930 percy, HenryAdvice to His Son ed. GB Harrison (London, 1930 http://www.cs.dartmouth.edu/~wbc/julia/biblio/biblio.htm
Extractions: BIBLIOGRAPHY AcM Acta musicologica AnMc Analecta Musicologica AnnM Annales musicologiques CMc Current Musicology EMc Early Music FAM Fontes artis musicae JAMS Journal of the American Musicological Society JLSA Journal of the Lute Society of America JRMA Journal of the Royal Musical Association LSJ Lute Society Journal The Lute MA The Musical Antiquary MD Musica Disciplina Music and Letters MMEME Music in Medieval and Early Modern Europe MQ The Musical Quarterly MR The Music Review MT The Musical Times PRMA Proceedings of the Royal Musical Association RISM SIMG TL The Library Abbot 1975 Abbot, Djilda and Segerman, Eric: 'The Cittern in England before 1700' LSJ xvii (1975), 24 Adriansen 1584 Adriansen, Emanuel: Pratum musicum (Antwerp, 1584) Adriansen 1592 Novum pratum musicum (Antwerp, 1592) Adriansen 1600 Pratum musicum (Antwerp, 1600) Alexander 1978 Alexander, Jonathan J G: The Decorated Letter (London, 1978) Alexander/Gibson 1976 Alexander, Jonathan J G and Gibson, Margaret T: Medieval Learning and Literature, Essays presented to Richard William Hunt (Oxford, 1976)
Renaissance Bibliography *Adams, percy G., Travelers and Travel Liars, 1660 1 (1984). heawood, E., A HithertoUnknown World Map of AD 1506 , The Geographical Journal, October 1923. http://www.henry-davis.com/MAPS/Ren/Ren1/Bib4.html
Theorems And Thoughts A proof was announced in 1879 by Alfred Kempe to great acclaim, but elevenyears later percy heawood revealed a fatal error in his argument. http://math.colstate.edu/Maxclub/Theorems.htm
Extractions: Dr. Eugen Ionascu The Four Color Theorem Theorem 1 Given a map drawn in the plane we can color the countries with red, green, blue and orange in such a way that any two adjacent countries have different colors. Here countries are assumed to be connected; we disallow the United States, for example, as Alaska and Hawaii are separated from the main body of the country. Two countries are only considered to be adjacent if they have a common boundary of nonzero length, not if they just touch at a single point. For a detailed history of this problem, see the St Andrews history of mathematics site. Briefly, Francis Guthrie conjectured in 1852 that the result was true, but was unable to prove it. Over the next 27 years a number of powerful mathematicians such as
ThinkQuest Library Of Entries Conjecture in 1890. percy John heawood, a lecturer at Durham England,published a paper called Map colouring theorem. In it he states http://library.thinkquest.org/C006364/ENGLISH/problem/four.htm
Extractions: The web site you have requested, A Taste of Mathematic , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to A Taste of Mathematic click here Back to the Previous Page The Site you have Requested ... click here to view this site Click image for the Site Languages : Site Desciption Welcome to A Taste of Mathematics.You will find the taste of mathematics here.The history of Mathematics,famous mathematicians,cxciting knowledge,the world difficult problems and also mathematics in our life... Browsing,thinking,enjoying,and have a good time here!
Chris with the problem. Except for one man, percy John heawood. He studiedKempes solution and encountered a fallacy. This would http://www.facstaff.bucknell.edu/udaepp/090/w3/chrisc.htm
Extractions: by Chris Cutillo The four-color conjecture has been one of several unsolved mathematical problems. From 1852 to this day, practically every mathematician has studied the problem long and hard, but to no avail. The conjecture looks as though it has been solved by Wolfgang Haken and Kenneth Appel, both of the University of Illinois. They have used computer technology to prove the conjecture. The calculation itself goes on for about 1200 hours. The staggering length of the computation of the proof is what creates some controversy in the mathematical world. You can see why this issue has been wreaking havoc for many years. It all started back in 1852 when Francis Guthrie was coloring a map of England. He wanted to know the least amount of colors, or chromatic number, it would take to color the map so no two adjacent regions are of the same color. He found the chromatic number to be four. He then studied arbitrary maps and wondered if all maps could be colored with four colors. He then passed this question on to his brother, Frederick.
Thepicturepoint HEAVY D 2. HEAVY PETTIN 1. heawood JOHN 2. HEAYBERD CAROL 1. HEB RUDOLF 2. HEBER REGINALD 1. HEBER RICARDO 3. HEBERpercy A 2. HEBER-percy V 1. http://www.topfoto.co.uk/engines/he.htm
GENUKI: 1891 CENSUS. RG12/1702/4 CROCKER Ella Rebecca Dau SF 5 y Scholar DEV Torquay CROCKER percy Raymont Son SM4 81 Teignmouth Rd-The Brake heawood Charles Head SM 57 y Own Means (Employer http://www.cs.ncl.ac.uk/genuki/DEV/Census.1891/V1702E04.html
Extractions: 1891 Census Contents This file has passed through Transcription, Checking and Validation stages. Records starting may contain significant doubts about some part of the person or address information, or the original may contain additional information. Researchers are advised to view original source material for verification. Brian Randell, 11 Jan 2003 Note:
Backstage-Reading Programmes 1983 Boothe, Michael, Mr. actor Ryan, Joan, Miss choreographer heawood, John, Mr actor Mtwa, percy, Mr. actor Ngema, Mbongeni, Mr. director Simon, Barney http://library.ukc.ac.uk/library/special/Programmes/PRG1983.HTM
Extractions: TEMPLEMAN LIBRARY UNIVERSITY OF KENT AT CANTERBURY Theatre Collections : Programme Collection Backstage : Jack Reading's Programmes 1983 UKC/PRG/READ/OPE NAT : F174480 Publicity flier advertising WHERE THE WILD THINGS ARE to be produced at the National. National Theatre, Upper Ground, South Bank, London, England WHERE THE WILD THINGS ARE
Cambridge Theatre, London Programmes Miss, 19061996 actor Clarke, E. Bellenden, Mr. actor percy, Esme, Miss Mr. actor Warwick, Norman, Mr. actor Szigeti, Rudi, Mr. actor heawood, John, Mr http://library.ukc.ac.uk/library/special/Programmes/CAMBRID.HTM
Extractions: TEMPLEMAN LIBRARY UNIVERSITY OF KENT Theatre Collections : London Theatres Cambridge Theatre, Earlham Street, Seven Dials, Camden UKC/PRG/BUCK/THE CAM : F187251 Theatre programme for a musical play seen at the Cambridge Theatre, London, entitled CAGE ME A PEACOCK. Cambridge Theatre, Earlham Street, Seven Dials, Camden, London, England manager : Tanner, Cyril, Mr. 1933 (circa) play 1 CAGE ME A PEACOCK
