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Full Description
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.
Contents
Preface; Twenty key icons of mathematics; 1. The Bride's Chair; 2. Zhou Bi Suan Jing; 3. Garfield's trapezoid; 4. The semicircle; 5. Similar figures; 6. Cevians; 7. The right triangle; 8. Napoleon's triangles; 9. Arcs and angles; 10. Polygons with circles; 11. Two circles; 12. Venn diagrams; 13. Overlapping figures; 14. Yin and yang; 15. Polygonal lines; 16. Star polygons; 17. Self-similar figures; 18. Tatami; 19. The rectangular hyperbola; 20. Tiling; Solutions to the challenges; References; Index; About the authors.
