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Titlebook: Geometric Problems on Maxima and Minima; Titu Andreescu,Oleg Mushkarov,Luchezar Stoyanov Textbook 2006 Birkhäuser Boston 2006 Convexity.Eu

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发表于 2025-3-21 17:05:25 | 显示全部楼层 |阅读模式
书目名称Geometric Problems on Maxima and Minima
编辑Titu Andreescu,Oleg Mushkarov,Luchezar Stoyanov
视频video
概述Presents hundreds of extreme value problems, examples, and solutions primarily through Euclidean geometry.Unified approach to the subject, with emphasis on geometric, algebraic, analytic, and combinat
图书封面Titlebook: Geometric Problems on Maxima and Minima;  Titu Andreescu,Oleg Mushkarov,Luchezar Stoyanov Textbook 2006 Birkhäuser Boston 2006 Convexity.Eu
描述.Questions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a uniquely intuitive approach to the subject: it presents hundreds of extreme value problems, examples, and solutions primarily through Euclidean geometry...Written by a team of established mathematicians and professors, this work draws on the authors’ experience in the classroom and as Olympiad coaches. By exposing readers to a wealth of creative problem-solving approaches, the text communicates not only geometry but also algebra, calculus, and topology. Ideal for use at the junior and senior undergraduate level, as well as in enrichment programs and Olympiad training for advanced high school students, this book’s breadth and depth will appeal to a wide audience, from secondary school teachers and pupils to graduate students, professional mathematicians, and puzzle enthusiasts..
出版日期Textbook 2006
关键词Convexity; Euclidean geometry; Maxima; algebra; calculus; extrema; ksa; maximum; minimum; optimization; combin
版次1
doihttps://doi.org/10.1007/0-8176-4473-3
isbn_softcover978-0-8176-3517-6
isbn_ebook978-0-8176-4473-4
copyrightBirkhäuser Boston 2006
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Thilo Büsching,Gabriele Goderbauer-Marchnerimeter. The best-known example of such a problem is the classical isoperimetric problem, where of all plane regions (bounded by a simple closed curve) with a given perimeter one wants to find the one of maximal area. Its solution is given by the so-called isoperimetric theorem, which we state in three equivalent ways.
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Methods for Finding Geometric Extrema,The transformations involved are the well-known symmetry with respect to a line or a point, rotation, and dilation. Apart from this, in some space geometry problems we are going to use symmetry through a plane, rotation about a line, and space dilation. We refer the reader to [17 ]or [22 ] for general information about geometric transformations.
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Textbook 2006 to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a uniquely intuitive approach to the subject: it presents hundreds of extreme value problems, examples, and
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Hints and Solutions to the Exercises,myqaeeacaGLOaGaayzkaaGaeyypa0ZaaSaaae% aacqaIXaqmaeaacqaIYaGmaaWaaeWaaeaacqWGdbWqcqWGbbqqcqGH% RaWkcqWGdbWqcqWGcbGqaiaawIcacaGLPaaacqGGUaGlaaa!56EE![CM = frac{1}{2}CC‘ leqslant frac{1}{2}left( {CA + C‘A} ight) = frac{1}{2}left( {CA + CB} ight).]
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978-0-8176-3517-6Birkhäuser Boston 2006
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