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This book is about beautiful mathematical concepts and creations. Mathematical ideas have an aesthetic appeal that can be appreciated by those who have the time and dedication to investigate. Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions, and unsolved problems. Readers will investigate exciting mathematical topics ranging from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared. Do you know that a lemniscate curve is the circular inversion of a hyperbola? That Sierpinski's triangle has fractal dimension 1.585....' That a regular septagon can be constructed with straightedge, compass, and an angle trisector? Do you know how to prove Lagrange s theorem that every positive integer is the sum of four squares? Can you find the first three digits of the millionth Fibonacci number? Discover the keys to these and many other mathematical problems. In each case, the mathematics is compelling, elegant, simple, and beautiful. Who should read this book? There is something new for any mathematically-minded person. High school and college students will find motivation for their mathematical studies. Professional mathematicians will find fresh examples of mathematical beauty to pass along to others. Within each chapter, the topics require progressively more prerequisite knowledge. An appendix gives background definitions and theorems, while another gives challenging exercises (with solutions).

Tabla de contenidos provista por Syndetics

• Preface
• 1 Imaginative words
• 2 Intriguing images
• 3 Captivating formulas
• 4 Delightful theorems
• 5 Pleasing proofs
• 6 Elegant solutions
• 7 Creative problems
• Appendix A Harmonious foundations
• Appendix B Eye-opening explorations

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CHOICE Review

Beautiful Mathematics is a visually stimulating book, even though the text and images are in black and white. Erickson (Truman State Univ.) is the author/coauthor of several mathematics books, including Pearls of Discrete Mathematics (CH, Apr'10, 47-4469) and Aha! Solutions (CH, May'09, 46-5081). Here he uses graphs, tables, geometric shapes, matrices, and other images to show a variety of concepts. For example, in chapter 5 he uses a tessellation when discussing the Pythagorean theorem. Each chapter is broken into sections that focus on specific topics. In chapter 2, "Intriguing Images," Erickson discusses and displays different illustrations he finds fascinating. A nice feature is that even though this chapter contains ten sections, the chapter is only 12 pages from start to finish, making it easy for browsing. Two appendixes conclude the work. Appendix A gives theorems, definitions, and other background information. Appendix B is broken into two parts, "Problems" and "Solutions," and refers to topics discussed earlier. This book would make a good supplemental resource for students in upper-level math courses. Summing Up: Recommended. Upper-division undergraduates and above. K. D. Holton Tallahasee Community College