Beautiful Mathematics
Published on 30. December 2011
Book
Hardback
191 pages
978-0-88385-576-8 (ISBN)
Description
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).
Reviews / Votes
Beautiful Mathematics is a collection of interesting mathematical explorations published by the MAA. If you find the following questions (many of which are new to me) intriguing then you'll probably enjoy this book. 1. Do you know the dimension of Sirpienski's Triangle 2. Have you ever explored squaring maps? 3. What is the Riemann Sphere? 4. Can you find a formula that associates Fibonacci numbers and Pi? 5. Can a square be inscribed in any triangle? 6. What are the first three digits of the millionth Fibonacci number? 7. Do you know how to construct a regular heptagon using a straight edge, compass, and angle trisecting device? 8. Can you prove Lagrange's Theorem, that every positive integer is the sum of four squares? 9. How many triangles are there of perimeter n, where n is an integer, the sides are all integer lengths and the triangles are incongruent? ""Beautiful Mathematics"" has nearly 100 challenging investigations, most with elegant solutions presented. Topics include words, images, formulas, theorems, proofs, solutions, and unsolved problems."" - Sol Lederman, Wild About Math""There is probably no mathematician who has never been surprised by a mathematical statement or has not been delighted in a mathematical argument. For those who know, mathematics has beauty, elegance, mystery, and of course surprise. Most mathematicians chose this endeavor after having experienced such a moment of enlightenment. Beautiful Mathematics offers ample opportunity for such an experience to everyone with even a slightest interest in mathematics. This book is a collection of short (1-2 pages long) vignettes that illuminate mathematical beauty from various angles. Mathematicians use imaginative words: lemniscate (a woolen ribbon used in fastening a garland to someone's head), waterfall of primes, golden ration, triangular numbers... They visualize intriguing images: binary trees, projective plane, two-colored graph, and come up with captivating formulas: series and products for n, the Riemann Zeta function, the Jacobi identity. Mathematicians prove delightful theorems: Morley's, Monge's, Minkowski's. Mathematics has pleasing proofs and elegan solutions; to pose an interesting problem requires creativity; all of that stands on harmonious foundations. The book ends with eye-opening explorations and these come with solutions, to boot. If pressed for an extra rubric, I would consider a separate section on ""Engaging Games,"" as this is something that mathematicians are preoccupied with-literally and metaphorically. (Not that the book entirely overlooks that side of mathematical activities. There are chapters on zero-sum games, nonattacking queens game, transversal achievement game-and more.)"" - Alex Bogomolny, MAA Reviews
""No mathematician needs to be told that there is a great deal of beauty in mathematics, although it is still nice to be reminded of it once in awhile. This book will do a great deal of that.There is no underlying theme or area of emphasis, there is great breadth of coverage. One could justly call it mathematical ramblings. The only requirement is that the mathematics be elegant and relatively simple. Topics range from complex numbers, to the google and the Centillion, to hypercubes and taxicab numbers. Problems are posed that range from the simple to the currently unsolved, 31 problems referencing the topics appear in an appendix and solutions are included.If you are a teacher of mathematics at the college level and are interested in presenting material that does not appear in the standard texts, then this is a book that you should look at. Most instructors of undergraduate classes should be able to find a problem suitable for inclusion in the class they are currently teaching."" - Charles Ashbacher, Journal of Recreational Mathematics
More details
Series
Language
English
Place of publication
Washington DC
United States
Target group
Professional and scholarly
Dimensions
Height: 261 mm
Width: 183 mm
Thickness: 15 mm
Weight
490 gr
ISBN-13
978-0-88385-576-8 (9780883855768)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Martin Erickson is a professor of mathematics at Truman State University.
Content
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.