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Four Colors Suffice: How the Map Problem Was Solved
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. .
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God Alone Suffices
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Working prosodies: finding what will suffice.(Prosody & poetry: a panel): An article from: The Antioch Review
This digital document is an article from The Antioch Review, published by Antioch Review, Inc. on January 1, 2004. The length of the article is 3634 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser. Citation DetailsTitle: Working prosodies: finding what will suffice.(Prosody & poetry: a panel) Author: Eleanor Berry Publication:The Antioch Review (Refereed) Date: January 1, 2004 Publisher: Antioch Review, Inc. Volume: 62 Issue: 1 Page: 104(10) Distributed by Thomson Gale.
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Pelvic muscle education suffices for urge incontinence. (May Avoid Expensive Biofeedback Approach).: An article from: Internal Medicine News
This digital document is an article from Internal Medicine News, published by International Medical News Group on February 1, 2002. The length of the article is 983 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser. Citation DetailsTitle: Pelvic muscle education suffices for urge incontinence. (May Avoid Expensive Biofeedback Approach). Author: Miriam E. Tucker Publication:Internal Medicine News (Magazine/Journal) Date: February 1, 2002 Publisher: International Medical News Group Volume: 35 Issue: 3 Page: 13(1) Distributed by Thomson Gale.
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Less-painful tests may suffice in first UTIs.(Infectious Diseases): An article from: Pediatric News
This digital document is an article from Pediatric News, published by Thomson Gale on February 1, 2007. The length of the article is 820 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser. Citation DetailsTitle: Less-painful tests may suffice in first UTIs.(Infectious Diseases) Author: Patrice Wendling Publication:Pediatric News (Magazine/Journal) Date: February 1, 2007 Publisher: Thomson Gale Volume: 41 Issue: 2 Page: 22(1) Distributed by Thomson Gale.
Price: $9.95
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Noninvasive indices may suffice to evaluate ulcerative colitis.(Digestive Disorders): An article from: Family Practice News
This digital document is an article from Family Practice News, published by Thomson Gale on October 15, 2005. The length of the article is 493 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser. Citation DetailsTitle: Noninvasive indices may suffice to evaluate ulcerative colitis.(Digestive Disorders) Author: Heidi Splete Publication:Family Practice News (Magazine/Journal) Date: October 15, 2005 Publisher: Thomson Gale Volume: 35 Issue: 20 Page: 51(1) Distributed by Thomson Gale.
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What Will Suffice -Contemporary American Poets on the Art of Poetry
Poets are generally at ease discussing the works of other poets and discussing the work of poetry in general But rarely do we find them so quickly predisposed to explicating their own poems, preferring instead to let their poems speak for themselves (otherwise, why write them?). In What Will Suffice, poets Christopher Buckley and Christopher Merrill, following up on Wallace Stevens's assertion that "poetry is the subject of the poem," have culled ars-poetica poems from more than 100 contemporary poets. These investigations into the art of poetry range from the oblique to the obvious, and nearly all of them are accompanied by textual explications by the poets that touch on topics such as faith, irony, mystery, music, imagination, language, curiosity, inspiration, religion, magic, grace, passion, observation, memory, and myth. This generous gesture on the part of the poets could have been accompanied by a greater generosity on the part of the publisher: the comments are set in puny type with cramped leading..
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