Beautiful Mathematics

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MAA, Dec 22, 2011 - Mathematics - 177 pages
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).

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very good book.

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In "Beautiful Mathematics," pages 106-108, section 5.17, "A Group of Operations," Martin Erickson does not acknowledge any source. That section, on a group of 322,560 permutations generated by permuting the rows, columns, and quadrants of a 4x4 array, is based on the Cullinane diamond theorem. See that theorem (published in an AMS abstract in 1979) at and, and elsewhere on the Web. Details of the proof given by Erickson may be found in "Binary Coordinate Systems," a 1984 article on the Web at 

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About the author (2011)

Martin Erickson was born in Detroit, MI in 1963. He graduated with High Honors from the University of Michigan in 1985 and received his Ph.D. at the University of Michigan in 1987. He is a professor of mathematics at Truman State University. He has written several acclaimed mathematics books, including "Aha! Solutions" (MAA) and "Introduction to Number Theory" (with Anthony Vazzana, CRC Press). He is a member of the Mathematical Association of America and the American Mathematical Society.

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