
Charming Proofs
A Journey Into Elegant Mathematics
Mathematical Association of America (MAA) (Publisher)
Published on 31. October 2010
Book
Hardback
316 pages
978-0-88385-348-1 (ISBN)
Description
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 present 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, to share their discoveries with others, and to become involved in the process of creating new proofs.
Charming Proofs is organized as follows. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming. Topics include the integers, selected real numbers, points in the plane, triangles, squares and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, three-dimensional geometry, etc. At the end of each chapter are some challenges that will draw the reader into the process of creating charming proofs. There are over 130 such challenges.
Charming Proofs concludes with solutions to all of the challenges, references, and a complete index. As in the authors' previous books with the MAA (Math Made Visual and When Less Is More), secondary school, college, and university teachers may wish to use some of the charming proofs in their classrooms to introduce their students to mathematical elegance. Some may wish to use the book as a supplement in an introductory course on proofs, mathematical reasoning, or problem solving.
Charming Proofs is organized as follows. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming. Topics include the integers, selected real numbers, points in the plane, triangles, squares and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, three-dimensional geometry, etc. At the end of each chapter are some challenges that will draw the reader into the process of creating charming proofs. There are over 130 such challenges.
Charming Proofs concludes with solutions to all of the challenges, references, and a complete index. As in the authors' previous books with the MAA (Math Made Visual and When Less Is More), secondary school, college, and university teachers may wish to use some of the charming proofs in their classrooms to introduce their students to mathematical elegance. Some may wish to use the book as a supplement in an introductory course on proofs, mathematical reasoning, or problem solving.
More details
Edition
UK edition
Language
English
Place of publication
Washington DC
United States
Target group
College/higher education
Product notice
sewn/stitched
Cloth over boards
Illustrations
269 b/w illus. 3 tables 149 exercises
Dimensions
Height: 236 mm
Width: 154 mm
Thickness: 25 mm
Weight
551 gr
ISBN-13
978-0-88385-348-1 (9780883853481)
Schweitzer Classification
Persons
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).
Content
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.
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.