01607cam a22002417a 4500008004100000020001800041020001500059040000800074050002300082100002000105245009100125260007000216300001900286490005200305505033200357505001700689518001500706520054800721650003101269650001901300650002501319700002101344081120s2009    dcuac    b    001 0 eng d  a9780883853429  a0883853426  aSDU00aQA295bA461 W 20091 aAlsina, Claudi.10aWhen less is more :bvisualizing basic inequalities /cClaudi Alsina, Roger B. Nelsen.  a[Washington, D.C.] :bMathematical Association of America,c2009.  a181 p. :bill.1 aThe Dolciani mathematical expositions ;vno. 360 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.0 aHKBU library  aYT2025 M10  aThe 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 0aInequalities (Mathematics) 0aVisualization. 0aGeometrical drawing.1 aNelsen, Roger B.