When less is more : visualizing basic inequalities / Claudi Alsina, Roger B. Nelsen.

Format:

Book

Author/Creator:

Alsina, Claudi, author.

Contributor:

Nelsen, Roger B.

Series:

Dolciani mathematical expositions ; no. 36.

Dolciani Mathematical Expositions, v. 36

Language:

English

Subjects (All):

Inequalities (Mathematics).

Visualization.

Geometrical drawing.

Physical Description:

1 online resource (xix, 181 pages : illustrations, portraits)

Place of Publication:

[Washington, D.C.] : Mathematical Association of America, c2009.

System Details:

Mode of access : World Wide Web

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 of the book some inequalities are more analytical in their statements as well as their proofs. --from publisher description

Contents:

Preface Introduction Chapter 1. Representing positive numbers as lengths of segments Chapter 2. Representing positive numbers as areas or volumes Chapter 3. Inequalities and the existence of triangles Chapter 4. Using incircles and circumcircles Chapter 5. Using reflections Chapter 6. Using rotations Chapter 7. Employing non-isometric transformations Chapter 8. Employing graphs of functions Chapter 9. Additional topics Solutions to the Challenges References Solutions to the Challenges References

Notes:

Includes bibliographical references (pages 171-177) and index.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Description based on print version record.

Other Format:

Print version: Alsina, Claudi. When less is more :

ISBN:

9781614442028 (online)

Access Restriction:

Restricted for use by site license.