Charming Proofs: A Journey into Elegant Mathematics

Charming Proofs: A Journey into Elegant Mathematics

by Claudi Alsina, Roger B. Nelsen
     
 

ISBN-10: 0883853485

ISBN-13: 9780883853481

Pub. Date: 01/27/2011

Publisher: Mathematical Association of America

Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs ‘there is a very high degree of unexpectedness, combined with inevitability and economy'. Charming Proofs presents a collection of remarkable proofs in elementary mathematics that are

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Overview

Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs ‘there is a very high degree of unexpectedness, combined with inevitability and economy'. Charming Proofs presents a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, and to develop the ability to create proofs themselves. The authors consider proofs from topics such as geometry, number theory, inequalities, plane tilings, origami and polyhedra. Secondary school and university teachers can use this book to introduce their students to mathematical elegance. More than 130 exercises for the reader (with solutions) are also included.

Product Details

ISBN-13:
9780883853481
Publisher:
Mathematical Association of America
Publication date:
01/27/2011
Series:
Dolciani Mathematical Expositions Series
Edition description:
New Edition
Pages:
316
Product dimensions:
5.98(w) x 8.98(h) x 0.91(d)

Table of Contents

Preface; Introduction; 1. A garden of integers; 2. Distinguished numbers; 3. Points in the plane; 4. The polygonal playground; 5. A treasury of triangle theorems; 6. The enchantment of the equilateral triangle; 7. The quadrilaterals' corner; 8. Squares everywhere; 9. Curves ahead; 10. Adventures in tiling and coloring; 11. Geometry in three dimensions; 12. Additional theorems, problems and proofs; Solutions to the challenges; References; Index; About the authors.

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