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Vældigt underholdende fortælling om firfarveteoremet og hvordan man kan slå det ihjel med en computer.
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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.… (more)
User reviews
The writing overall was fine -- not brilliant, not poor, but somewhere in the middle. For some of the mathematics, the discussion was a bit unclear and hard to follow. (Yes, the methods used by various attempted proofs are difficult topics, but even having a decent mathematical background, I had to reread several pages to understand what he was trying to say.) The diagrams were terrific! The history was well researched with notes and a bibliography.
On the down side, the book lacked somewhat. As mentioned above, some areas were obtuse. Also some topics, such as why this is an important problem and not just a "let's see if we can prove it" type of problem, were alluded to but never really discussed. Wilson stated several places that the math used to solve this problem led to other important results, such as...well, he never says. Also, the final section as to whether or not the proof is valid felt like it was added later, without much enthusiasm. Proof by exhaustive computer search is a very interesting question -- is it really a proof? I understand that a thorough discussion would involve a lot of discussion of computer programming, but this book (as evidenced by the level of math when discussing the historic proofs) is aimed for a mathematical literate audience that could understand the basics of the computer issues.
Overall, the history part of the book was fine, but the "we have a proof" section was lacking. I will probably read it again at sometime, but not terribly soon.
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Omslaget viser en ø formet som et firtal og inddelt i lande.
Indskannet omslag - N650U - 150 dpi
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Pages
DDC/MDS
500 |