Map Coloring Polyhedra And The Fourcolor Problem PDF Download
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Author | : David Barnette |
Publisher | : MAA Press |
Total Pages | : 186 |
Release | : 1983 |
Genre | : Mathematics |
ISBN | : |
Download Map Coloring, Polyhedra, and the Four-color Problem Book in PDF, ePub and Kindle
Author | : David W. Barnette |
Publisher | : American Mathematical Soc. |
Total Pages | : 168 |
Release | : 1984-03-01 |
Genre | : Mathematics |
ISBN | : 1470457172 |
Download Map Coloring, Polyhedra and the FourColor Problem Book in PDF, ePub and Kindle
Author | : David Wilmot Barnette |
Publisher | : |
Total Pages | : 168 |
Release | : 1983 |
Genre | : |
ISBN | : 9780883853009 |
Download Map Coloring, Polyhedra, and the Four-color Problem Book in PDF, ePub and Kindle
Author | : Robin Wilson |
Publisher | : Princeton University Press |
Total Pages | : 218 |
Release | : 2021-10-12 |
Genre | : Mathematics |
ISBN | : 0691237565 |
Download Four Colors Suffice Book 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. This new edition features many color illustrations. It also includes a new foreword by Ian Stewart on the importance of the map problem and how it was solved.
Author | : Rudolf Fritsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 269 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461217202 |
Download The Four-Color Theorem Book 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.
Author | : Rudolf Fritsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 294 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 9780387984971 |
Download The Four-Color Theorem Book in PDF, ePub and Kindle
This elegant little book discusses a famous problem that helped to define the field now known as graph theory: what is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries are. Many famous mathematicians have worked on the problem, but the proof eluded formulation until the 1970s, when it was finally cracked with a brute-force approach using a computer. The Four-Color Theorem begins by discussing the history of the problem up to the new approach given in the 1990s (by Neil Robertson, Daniel Sanders, Paul Seymour, and Robin Thomas). The book then goes into the mathematics, with a detailed discussion of how to convert the originally topological problem into a combinatorial one that is both elementary enough that anyone with a basic knowledge of geometry can follow it and also rigorous enough that a mathematician can read it with satisfaction. The authors discuss the mathematics and point to the philosophical debate that ensued when the proof was announced: just what is a mathematical proof, if it takes a computer to provide one - and is such a thing a proof at all?
Author | : Thomas L. Saaty |
Publisher | : |
Total Pages | : 240 |
Release | : 1977 |
Genre | : Mathematics |
ISBN | : |
Download The Four-color Problem Book in PDF, ePub and Kindle
Author | : |
Publisher | : Academic Press |
Total Pages | : 277 |
Release | : 2011-08-29 |
Genre | : Mathematics |
ISBN | : 0080873391 |
Download The Four-Color Problem Book in PDF, ePub and Kindle
The Four-Color Problem
Author | : Peter R. Cromwell |
Publisher | : Cambridge University Press |
Total Pages | : 498 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780521664059 |
Download Polyhedra Book in PDF, ePub and Kindle
Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating.
Author | : David S. Richeson |
Publisher | : Princeton University Press |
Total Pages | : 336 |
Release | : 2019-07-23 |
Genre | : Mathematics |
ISBN | : 0691191999 |
Download Euler's Gem Book in PDF, ePub and Kindle
How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.