Charming Proofs
Mathematical Association of America (Verlag)
978-0-88385-348-1 (ISBN)
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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.
Claudi Alsina received his BA and Ph.D. in Mathematics from the University of Barcelona. His postdoctoral studies were at the University of Massachusetts, Amherst. As Professor of Mathematics at the Technical University of Catalonia, Claudi has delivered a wide range of research papers, publications and lectures on mathematics and mathematics education. His latest books include Associative Functions (co-authored with M. J. Frank and B. Schweizer, WSP, 2006) and Math Made Visual (co-authored with Roger B. Nelsen, MAA, 2006).
Roger B. Nelsen received his BA in Mathematics from DePauw University and his Ph.D. from Duke University in 1969. He taught mathematics and statistics at Lewis and Clark College for forty years before his retirement in 2009. His previous books include Proofs Without Words (MAA, 1993) and An Introduction to Copulas (Springer, 1999).
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.
| Erscheint lt. Verlag | 27.1.2011 |
|---|---|
| Reihe/Serie | Dolciani Mathematical Expositions |
| Zusatzinfo | 269 b/w illus. 3 tables 149 exercises |
| Verlagsort | Washington |
| Sprache | englisch |
| Maße | 152 x 228 mm |
| Gewicht | 540 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Mathematik / Informatik ► Mathematik ► Mathematische Spiele und Unterhaltung | |
| ISBN-10 | 0-88385-348-5 / 0883853485 |
| ISBN-13 | 978-0-88385-348-1 / 9780883853481 |
| Zustand | Neuware |
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