In one sense, the problem of finding the densest packing of congruent circles in a square is easy to understand. But on closer inspection, this problem reveals itself to be an interesting challenge of discrete and computational geometry with all its surprising structural forms and regularities. This book summarizes results achieved in solving the circle packing problem over the past few years, providing the reader with a comprehensive view of both theoretical and computational achievements. Typically illustrations of problem solutions are shown, elegantly displaying the results obtained.
Beyond the theoretically challenging character of the problem, the solution methods developed in the book also have many practical applications.
One especially important feature of the book is the inclusion on an enclosed CD of all the open source programming codes used. Since the codes can be worked with directly, they will enable the reader to improve on them and solve problem instances that still remain challenging, or to use them as a starting point for solving related application problems.
In clear, easy-to-grasp language, the author covers many of the topics that you will need to know in order to launch and run a successful business venture.
Hikernut's Grand Canyon Companion A Guide To Hiking And Backpacking The Most Popular Trails Into The Canyon
Covering the Central Corridor Trails (including Bright Angel, South Kaibab, and North Kaibab Trails), which provide spectacular views and are among the most popular routes, this guide has everything potential hikers need to safely navigate the canyon. Over 250 people are rescued from the Inner Canyon each year. Don't become a statistic-read this book! Along with trail descriptions, a comprehensive gear list, rules and restrictions, hiking tips and trip planning ideas, award-winning author Brian J. Lane offers practical advice gleaned from over twenty years of hiking in and around the Grand Canyon and throughout the United States and Canada. Packed with beautiful full-color photos, illustrations, charts, tables and maps, this book is perfect for first time canyon explorers, and was chosen by the IBPA as a Benjamin Franklin Award Winning Finalist in 2008.
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