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Icons of mathematics [electronic resource] : an exploration of twenty key images / Claudi Alsina, Roger B. Nelsen.

By: Contributor(s): Material type: TextTextSeries: Dolciani mathematical expositions ; no. 45.Publication details: [Washington, D.C.] : Mathematical Association of America, c2011.Description: 1 online resource (xvii, 327 p.) : ill., portsISBN:
  • 9780883859865 (electronic bk.)
  • 0883859866 (electronic bk.)
  • 0883853523
  • 9780883853528
Subject(s): Genre/Form: Additional physical formats: Print version:: Icons of mathematics.DDC classification:
  • 516.204 23
LOC classification:
  • QA466 .A47 2011
Online resources:
Contents:
The bride's chair -- Zhou Bi Suan Jing -- Garfield's trapezoid -- The semicircle -- Similar figures -- Cevians -- The right triangle -- Napoleon's triangles -- Arcs and angles -- Polygons with circles -- Two circles -- Venn diagrams -- Overlapping figures -- Yin and yang -- Polygonal lines -- Star polygons -- Self-similar figures -- Tatami -- The rectangular hyperbola -- Tiling -- Solutions to the challenges.
Summary: Certain geometric diagrams play a crucial role in visualizing mathematical proofs. Twenty of these icons of mathematics are presented in this book, where the authors explore the mathematics within them and the mathematics that can be created from them. A chapter is devoted to each icon, illustrating its presence in real life, its primary mathematical characteristics and how it plays a central role in visual proofs of a wide range of mathematical facts. Among these are classical results from plane geometry, properties of the integers, means and inequalities, trigonometric identities, theorems from calculus and puzzles from recreational mathematics. Each chapter concludes with a selection of challenges for the reader to explore further properties and applications of the icon. Those teaching undergraduate mathematics will find material here for problem solving sessions, as well as enrichment material for courses on proofs and mathematical reasoning.
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Includes bibliographical references (p. 309-319) and index.

The bride's chair -- Zhou Bi Suan Jing -- Garfield's trapezoid -- The semicircle -- Similar figures -- Cevians -- The right triangle -- Napoleon's triangles -- Arcs and angles -- Polygons with circles -- Two circles -- Venn diagrams -- Overlapping figures -- Yin and yang -- Polygonal lines -- Star polygons -- Self-similar figures -- Tatami -- The rectangular hyperbola -- Tiling -- Solutions to the challenges.

Description based on print version record.

Certain geometric diagrams play a crucial role in visualizing mathematical proofs. Twenty of these icons of mathematics are presented in this book, where the authors explore the mathematics within them and the mathematics that can be created from them. A chapter is devoted to each icon, illustrating its presence in real life, its primary mathematical characteristics and how it plays a central role in visual proofs of a wide range of mathematical facts. Among these are classical results from plane geometry, properties of the integers, means and inequalities, trigonometric identities, theorems from calculus and puzzles from recreational mathematics. Each chapter concludes with a selection of challenges for the reader to explore further properties and applications of the icon. Those teaching undergraduate mathematics will find material here for problem solving sessions, as well as enrichment material for courses on proofs and mathematical reasoning.

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