02318nam a2200385 a 4500 ebr10728521 CaPaEBR m o u cr cn||||||||| 081120s2009 dcuac sb 001 0 eng d 2008942145 9780883853429 (hbk.) 0883853426 (hbk.) 9781614442028 (e-book) CaPaEBR CaPaEBR (OCoLC)817962671 QA295 .A545 2009eb 515.26 22 Alsina, Claudi. When less is more [electronic resource] : visualizing basic inequalities / Claudi Alsina, Roger B. Nelsen. [Washington, D.C.] : Mathematical Association of America, c2009. xix, 181 p. : ill., ports. Dolciani mathematical expositions ; no. 36 Includes bibliographical references (p. 171-177) and index. Representing 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. The proofs in When Less is More are in the spirit of proofs without words, though most require at least a few words. The first inequalities presented in the book, such as the inequalities between the harmonic, geometric, and arithmetic mean, are familiar from analysis, but are given geometric proofs. The second and largest set of inequalities are geometric both in their statements and in their proofs. Toward the end of the book some inequalities are more analytical in their statements as well as their proofs--From publisher description. Electronic reproduction. Palo Alto, Calif. : ebrary, 2013. Available via World Wide Web. Access may be limited to ebrary affiliated libraries. Inequalities (Mathematics) Visualization. Geometrical drawing. Electronic books. local Nelsen, Roger B. ebrary, Inc. http://site.ebrary.com/lib/rucke/Doc?id=10728521 An electronic book accessible through the World Wide Web; click to view 37221 37221