Charming Proofs: A Journey into Elegant Mathematicsby Claudi Alsina, Roger B. Nelsen
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 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.
Table of ContentsPreface; 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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