00000cam a22000003i 4500 UP-1685594773861845868 Buklod 20110730111342.0 g||| | || || ta 180129s2009 dcuac rb |||1 u|eng d 9780883853429 (hbk.) (iLib)UPBAG-00008722536 BC-60825 Php4,245.75 DLC BAG rda eng QA 295 A47 2009 Alsina, Claudi author. When less is more visualizing basic inequalities Claudi Alsina, Roger B. Nelsen. Washington, D.C. Published and distributed by The Mathematical Association of America ©2009. xix, 181 pages illustrations, portraits 24 cm The Dolciani mathematical expositions no. 36 Includes bibliographical references (pages 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. Inequalities (Mathematics) Visualization. Geometrical drawing. Nelsen, Roger B. author. FO UPBAG UPBAG-MAIN QA 295 A47 2009 Book