eBook ISBN:  9781614442011 
Product Code:  DOL/42.E 
List Price:  $35.00 
MAA Member Price:  $26.25 
AMS Member Price:  $26.25 
eBook ISBN:  9781614442011 
Product Code:  DOL/42.E 
List Price:  $35.00 
MAA Member Price:  $26.25 
AMS Member Price:  $26.25 

Book DetailsDolciani Mathematical ExpositionsVolume: 42; 2010; 295 pp
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, threedimensional 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.

Table of Contents

Chapters

Chapter 1. A Garden of Integers

Chapter 2. Distinguished Numbers

Chapter 3. Points in the Plane

Chapter 4. The Polygonal Playground

Chapter 5. A Treasury of Triangle Theorems

Chapter 6. The Enchantment of the Equilateral Triangle

Chapter 7. The Quadrilaterals’ Corner

Chapter 8. Squares Everywhere

Chapter 9. Curves Ahead

Chapter 10. Adventures in Tiling and Coloring

Chapter 11. Geometry in Three Dimensions

Chapter 12. Additional Theorems, Problems, and Proofs


Additional Material

Reviews

The book covers a wide range of topics ... Many appeared in other publications, but together, they make a coherent collection that would please many a mathematics fan. As with their previous books, the authors supply each of the 12 chapters with challenge problems and the latter with solutions found at the end of the book. ... This makes the book of special interest to the middle and high school teachers of talented youth and the students themselves.
Alex Bogomolny, MAA Reviews


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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 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, threedimensional 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.

Chapters

Chapter 1. A Garden of Integers

Chapter 2. Distinguished Numbers

Chapter 3. Points in the Plane

Chapter 4. The Polygonal Playground

Chapter 5. A Treasury of Triangle Theorems

Chapter 6. The Enchantment of the Equilateral Triangle

Chapter 7. The Quadrilaterals’ Corner

Chapter 8. Squares Everywhere

Chapter 9. Curves Ahead

Chapter 10. Adventures in Tiling and Coloring

Chapter 11. Geometry in Three Dimensions

Chapter 12. Additional Theorems, Problems, and Proofs

The book covers a wide range of topics ... Many appeared in other publications, but together, they make a coherent collection that would please many a mathematics fan. As with their previous books, the authors supply each of the 12 chapters with challenge problems and the latter with solutions found at the end of the book. ... This makes the book of special interest to the middle and high school teachers of talented youth and the students themselves.
Alex Bogomolny, MAA Reviews