The Four Colour Theorem
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The Four Color Theorem
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Author : Rudolf Fritsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Four Color Theorem written by Rudolf Fritsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the university reform of the 1970s, the classical Faculty of Science of the venerable Ludwig-Maximilians-Universitat in Munich was divided into five smaller faculties. One was for mathematics, the others for physics, chemistry and pharmaceutics, biology, and the earth sciences. Nevertheless, in order to maintain an exchange of ideas between the various disciplines and so as not to permit the complete undermining of the original notion of "universitas,,,l the Carl-Friedrich-von-Siemens Foundation periodically invites the pro fessors from the former Faculty of Science to a luncheon gathering. These are working luncheons during which recent developments in the various disciplines are presented by means of short talks. The motivation for such talks does not come, in the majority of cases, from the respective subject itself, but from another discipline that is loosely affiliated with it. In this way, the controversy over the modern methods used in the proof of the Four-Color Theorem had also spread to disciplines outside of mathematics. I, as a trained algebraic topologist, was asked to comment on this. Naturally, I was acquainted with the Four-Color 1 A Latin word meaning the whole of something, a collective entirety. Vll viii Preface Problem but, up to that point, had never intensively studied it. As an outsider,2 I dove into the material, not so much to achieve any scientific progress with it but to make this already achieved objective more understandable.
The Four Colour Theorem
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Author : Ashay Dharwadker
language : en
Publisher: Institute of Mathematics
Release Date : 2000-08-05
The Four Colour Theorem written by Ashay Dharwadker and has been published by Institute of Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-05 with Mathematics categories.
We present a new proof of the famous four colour theorem using algebraic and topological methods. This proof was first announced by the Canadian Mathematical Society in 2000 and subsequently published by Orient Longman and Universities Press of India in 2008. Recent research in physics shows that this proof directly implies the Grand Unification of the Standard Model with Quantum Gravity in its physical interpretation and conversely the existence of the standard model of particle physics shows that nature applies this proof of the four colour theorem at the most fundamental level.
The Four Color Problem
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Author :
language : en
Publisher: Academic Press
Release Date : 2011-08-29
The Four Color Problem written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-29 with Mathematics categories.
The Four-Color Problem
Graphs Colourings And The Four Colour Theorem
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Author : Robert Wilson
language : en
Publisher: Oxford University Press
Release Date : 2002
Graphs Colourings And The Four Colour Theorem written by Robert Wilson and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This textbook for mathematics undergraduates, graduates and researchers discusses the proof of the four-colour theorem - one of the most famous of the long-standing mathematical problems solved in the 20th century.
Higgs Boson Mass Predicted By The Four Color Theorem
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Author : Ashay Dharwadker
language : en
Publisher: Institute of Mathematics
Release Date : 2009-12-28
Higgs Boson Mass Predicted By The Four Color Theorem written by Ashay Dharwadker and has been published by Institute of Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-28 with Mathematics categories.
We show that the mathematical proof of the four color theorem yields a perfect interpretation of the Standard Model of particle physics. The steps of the proof enable us to construct the t-Riemann surface and particle frame which forms the gauge. We specify well-defined rules to match the Standard Model in a one-to-one correspondence with the topological and algebraic structure of the particle frame. This correspondence is exact - it only allows the particles and force fields to have the observable properties of the Standard Model, giving us a Grand Unified Theory. In this paper, we concentrate on explicitly specifying the quarks, gauge vector bosons, the Standard Model scalar Higgs boson and the weak force field. Using all the specifications of our mathematical model, we show how to calculate the values of the Weinberg and Cabibbo angles on the particle frame. Finally, we present our prediction of the Higgs boson mass M = 126 GeV, as a direct consequence of the proof of the four color theorem.
Graph Theory 1736 1936
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Author : Norman Biggs
language : en
Publisher: Oxford University Press
Release Date : 1986
Graph Theory 1736 1936 written by Norman Biggs and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
First published in 1976, this book has been widely acclaimed both for its significant contribution to the history of mathematics and for the way that it brings the subject alive. Building on a set of original writings from some of the founders of graph theory, the book traces the historical development of the subject through a linking commentary. The relevant underlying mathematics is also explained, providing an original introduction to the subject for students. From reviews: 'The book...serves as an excellent examplein fact, as a modelof a new approach to one aspect of mathematics, when mathematics is considered as a living, vital and developing tradition.' (Edward A. Maziark in Isis) 'Biggs, Lloyd and Wilson's unusual and remarkable book traces the evolution and development of graph theory...Conceived in a very original manner and obviously written with devotion and a very great amount of painstaking historical research, it contains an exceptionally fine collection of source material, and to a graph theorist it is a treasure chest of fascinating historical information and curiosities with rich food for thought.' (Gabriel Dirac in Centaurus) 'The lucidity, grace and wit of the writing makes this book a pleasure to read and re-read.' (S. H. Hollingdale in Bulletin of the Institute of Mathematics and its Applications)
Maximal Planar Graph Theory And The Four Color Conjecture
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Author : Jin Xu
language : en
Publisher: Springer Nature
Release Date : 2025-05-23
Maximal Planar Graph Theory And The Four Color Conjecture written by Jin Xu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-23 with Computers categories.
This open access book integrates foundational principles with advanced methodologies concerning maximal planar graphs. It offers readers an exceptional examination of graph structures, chromatic polynomials, and the construction and proof techniques of the Four-Color Conjecture. It is tailored for researchers, educators, and students involved in graph theory, combinatorics, and computational mathematics. The book consists of nine meticulously developed chapters. It starts with fundamental concepts in graph theory and then advances to pioneering computational proofs and recursive formulas of the chromatic number related to maximal planar graphs. Notable features include comprehensive discharging techniques, innovative approaches for constructing graphs of various orders, and groundbreaking conjectures concerning tree-colorability and unique four-colorability. The concluding chapter introduces Kempe's changes, offering new insights into the dynamics of graph coloring. Whether you are an academic enhancing your theoretical knowledge or a student searching for clear explanations for complex concepts, this book provides essential tools for navigating and addressing some of the most intricate challenges in graph theory. Its rigorous analysis and computational techniques equip readers with the necessary skills to engage deeply with maximal planar graph problems, making it an indispensable resource for advancing research and practical applications. No prior knowledge is necessary; however, a foundational understanding of graph theory is advised. This opportunity presents a chance to explore innovative perspectives and methodologies that expand the horizons of mathematical inquiry and proof development.
The Four Color Problem
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Author : Thomas L. Saaty
language : en
Publisher:
Release Date : 1977
The Four Color Problem written by Thomas L. Saaty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.
Professor Stewart S Cabinet Of Mathematical Curiosities
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Author : Ian Stewart
language : en
Publisher: Basic Books
Release Date : 2009-01-06
Professor Stewart S Cabinet Of Mathematical Curiosities written by Ian Stewart and has been published by Basic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-06 with Mathematics categories.
Knowing that the most exciting math is not taught in school, Professor Ian Stewart has spent years filling his cabinet with intriguing mathematical games, puzzles, stories, and factoids intended for the adventurous mind. This book reveals the most exhilarating oddities from Professor Stewart's legendary cabinet. Inside, you will find hidden gems of logic, geometry, and probability-like how to extract a cherry from a cocktail glass (harder than you think), a pop-up dodecahedron, and the real reason why you can't divide anything by zero. Scattered among these are keys to Fermat's last theorem, the Poincaréonjecture, chaos theory, and the P=NP problem (you'll win a million dollars if you solve it). You never know what enigmas you'll find in the Stewart cabinet, but they're sure to be clever, mind-expanding, and delightfully fun.
Four Colors Suffice
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Author : Robin J. Wilson
language : en
Publisher: Princeton University Press
Release Date : 2002
Four Colors Suffice written by Robin J. Wilson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.