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 ...
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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.
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Seller's Description:
Fine with no dust jacket. 0883853485. With illustrations. Light shelfwear.; "Charming Proofs: A Journey into Elegant Mathematics" by Claudi Alsina and Roger B. Nelsen is a delightful exploration of mathematical elegance, showcasing proofs that not only solve problems but do so in beautifully simple and insightful ways. The book is a collection of proofs from various fields of mathematics, including geometry, algebra, number theory, and calculus. Each chapter is carefully curated to demonstrate the artistry and ingenuity inherent in mathematical reasoning. Alsina and Nelsen have crafted a book that is as educational as it is engaging. They present each proof with clear explanations and sufficient detail, making the concepts accessible to readers with a basic understanding of mathematics. The proofs are selected not only for their aesthetic appeal but also for their ability to illustrate fundamental mathematical principles in a clear and concise manner. This approach helps demystify complex ideas and invites readers to appreciate the creative aspects of mathematical thought. "Charming Proofs" is especially valuable for students and educators as it encourages a deeper understanding and appreciation of mathematics through its most elegant demonstrations. The book is peppered with historical anecdotes and insights that enrich the reader's experience, making the exploration of each proof more than just a study of steps and logic, but a journey through the rich history of mathematics.; Octavo; xxiv, 295 pages.