The Four-Color Theorem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Four-Color Theorem write by Rudolf Fritsch. This book was released on 2012-12-06. The Four-Color Theorem available in PDF, EPUB and Kindle. This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.
Four Colors Suffice
Four Colors Suffice - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Four Colors Suffice write by Robin J. Wilson. This book was released on 2002. Four Colors Suffice available in PDF, EPUB and Kindle. 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.
Every Planar Map is Four Colorable
Every Planar Map is Four Colorable - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Every Planar Map is Four Colorable write by Kenneth I. Appel. This book was released on 1989. Every Planar Map is Four Colorable available in PDF, EPUB and Kindle. In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained exposition accessible to a general mathematical audience. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a proof that four coloring can be accomplished in polynomial time.
The Four-color Problem
The Four-color Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Four-color Problem write by Thomas L. Saaty. This book was released on 1986. The Four-color Problem available in PDF, EPUB and Kindle.
Graphs, Colourings and the Four-Colour Theorem
Graphs, Colourings and the Four-Colour Theorem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Graphs, Colourings and the Four-Colour Theorem write by Robert A. Wilson. This book was released on 2002-01-24. Graphs, Colourings and the Four-Colour Theorem available in PDF, EPUB and Kindle. The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.
