When less is more : visualizing basic inequalities

✍ Scribed by Claudi Alsina; Roger B Nelsen

• Publisher: Mathematical Association of America
• Year: 2009
• Tongue: English
• Leaves: 204
• Series: Dolciani mathematical expositions, no. 36
• Category: Library

✦ Synopsis

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 Read more... 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