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When less is more : visualizing basic inequalities

Author: Claudi Alsina; Roger B Nelsen
Publisher: [Washington, D.C.] : Mathematical Association of America, ©2009.
Series: Dolciani mathematical expositions, no. 36.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Additional Physical Format: Print version:
Alsina, Claudi.
When less is more.
[Washington, D.C.] : Mathematical Association of America, ©2009
(DLC) 2008942145
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Claudi Alsina; Roger B Nelsen
ISBN: 9780883853429 0883853426
OCLC Number: 817962671
Description: 1 online resource (xix, 181 pages) : illustrations, portraits.
Contents: 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.
Series Title: Dolciani mathematical expositions, no. 36.
Responsibility: Claudi Alsina, Roger B. Nelsen.

Abstract:

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.

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