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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aWhen less is more $evisualizing basic inequalities /$fClaudi Alsina, Roger B. Nelsen$b[electronic resource]
210  1$aWashington :$cMathematical Association of America,$d2009.
215   $a1 online resource (xix, 181 pages) $cdigital, PDF file(s)
225 1 $aDolciani Mathematical Expositions, $vv. 36
225  0$aDolciani mathematical expositions ;$vno. 36
300   $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015).
311   $a0-88385-342-6 
320   $aIncludes bibliographical references (p. 171-177) and index.
327   $aRepresenting positive numbers as lengths of segments -- Representing positive numbers as areas or volumes -- Inequalities and the existence of triangles -- Using incircles and circumcircles -- Using reflections -- Using rotations -- Employing non-isometric transformations -- Employing graphs of functions -- Additional topics.
330   $aInequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too often, especially in secondary and collegiate mathematics, the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubt important, they don’t possess the richness and variety that one finds with inequalities.   The objective of this book is to illustrate how the use of visualization can be a powerful tool for better understanding some basic mathematical inequalities. Drawing pictures is a well-known method for problem solving, and the authors will convince you that the same is true when working with inequalities. They show how to produce figures in a systematic way for the illustration of inequalities and open new avenues to creative ways of thinking and teaching. In addition, a geometric argument cannot only show two things unequal, but also help the observer see just how unequal they are.   The concentration on geometric inequalities is partially motivated by the hope that secondary and collegiate teachers might use these pictures with their students. Teachers may wish to use one of the drawings when an inequality arises in the course. Alternatively, When Less Is More might serve as a guide for devoting some time to inequalities and problem solving techniques, or even as part of a course on inequalities.
410  0$aDolciani Mathematical Expositions
606   $aInequalities (Mathematics)
606   $aVisualization
606   $aGeometrical drawing
615  0$aInequalities (Mathematics)
615  0$aVisualization.
615  0$aGeometrical drawing.
676   $a515.26
700   $aAlsina$b Claudi$0309455
702   $aNelsen$b Roger B.
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910822033403321
996   $aWhen less is more$94046861
997   $aUNINA