Charming Proofs: A Journey into Elegant Mathematics [Alsina]

[mklabgr]

Charming Proofs: A Journey into Elegant Mathematics
Authors: Claudi Alsina and Roger B. Nelsen
Publication date: 2010
Publisher: Mathematical Association of America 
Series: Dolciani Mathematical Expositions, Vol. 42
Length: 295 pages in the current AMS listing
ISBN: 978-0-88385-348-1 

Summary

Charming Proofs is a collection devoted not merely to correct mathematical proofs, but to proofs that possess elegance, surprise, economy, and visual or conceptual beauty. Alsina and Nelsen take inspiration from G. H. Hardy's idea that a beautiful proof combines unexpectedness with inevitability and economy. Rather than developing one mathematical subject systematically, the book presents a tour through elementary mathematics, selecting arguments whose central ideas are unusually clever or satisfying. 

The mathematics ranges widely across number theory, geometry, real numbers, inequalities, polygons, triangles, quadrilaterals, squares, curves, tilings, coloring, origami, and three-dimensional geometry. Many proofs depend on an ingenious construction or a striking diagram rather than lengthy algebraic manipulation. The geometry is particularly prominent: entire chapters are devoted to triangle theorems, equilateral triangles, quadrilaterals, squares, curves, and spatial geometry. 

A major purpose of the book is to encourage the reader to move from admiring proofs to discovering them. Each chapter therefore ends with challenge problems—more than 130 challenges in total—and complete solutions appear later in the book. This makes it useful both as recreational mathematics and as supplementary material for courses in proof, mathematical reasoning, problem solving, or mathematical enrichment. The AMS specifically notes its usefulness for secondary-school, college, and university teachers.

Chapter structure
The twelve chapters are:

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 
    

BOOK