Paul J. Nahin, "Dr. Eulers Fabulous Formula: Cures Many Mathematical Ills"
English | 2006 | ISBN-10: 0691118221, 0691150370 | 416 pages | PDF | 2 MB
In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Eulers Fabulous Formula shares the fascinating story of this groundbreaking formula-long regarded as the gold standard for mathematical beauty-and shows why it still lies at the heart of complex number theory.
This book is the sequel to Paul Nahins An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems.
The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the books preface: To mathematicians ten thousand years hence, "Eulers formula will still be beautiful and stunning and untarnished by time."
"If you ever wondered about the beauties and powers of mathematics, this book is a treasure trove. Paul Nahin uses Eulers formula as the magic key to unlock a wealth of surprising consequences, ranging from number theory to electronics, presented clearly, carefully, and with verve."-Peter Pesic, St. Johns College
"The range and variety of topics covered here is impressive. I found many little gems that I have never seen before in books of this type. Moreover, the writing is lively and enthusiastic and the book is highly readable."-Des Higham, University of Strathclyde, Glasgow