How Euler Did Even More (Spectrum)

Sandifer has been studying Euler for decades and is one of the world s leading experts on his work. This volume is the second collection of Sandifer s How Euler Did It columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler's clever inventiveness and Sandifer's wonderful ability to explicate and put it all in context. Cover 1 Half Title 2 Copyright Page 3 Title Page 4 Series Page 5 Contents 10 Preface 12 Part I: Geometry 16 1 The Euler Line (January 2009) 18 2 A Forgotten Fermat Problem (December 2008) 25 3 A Product of Secants (May 2008) 33 4 Curves and Paradox (October 2008) 41 5 Did Euler Prove Cramer’s Rule? (November 2009—A Guest Column by Rob Bradley) 47 Part II: Number Theory 54 6 Factoring F5 (March 2007) 56 7 Rational Trigonometry (March 2008) 60 8 Sums (and Differences) that are Squares (March 2009) 67 Part III: Combinatorics 74 9 St. Petersburg Paradox (July 2007) 76 10 Life and Death – Part 1 (July 2008) 82 11 Life and Death – Part 2 (August 2008) 89 Part IV: Analysis 96 12 e, π and i: Why is “Euler” in the Euler Identity (August 2007) 98 13 Multi-zeta Functions (January 2008) 103 14 Sums of Powers (June 2009) 110 15 A Theorem of Newton (April 2008) 116 16 Estimating π (February 2009) 124 17 Nearly a Cosine Series (May 2009) 134 18 A Series of Trigonometric Powers (June 2008) 139 19 Gamma the Function (September 2007) 147 20 Gamma the Constant (October 2007) 151 21 Partial Fractions (June 2007) 156 22 Inexplicable Functions (November 2007) 161 23 A False Logarithm Series (December 2007) 169 24 Introduction to Complex Variables (May 2007) 175 25 The Moon and the Differential (October 2009—A Guest Column by Rob Bradley) 181 Part V: Applied Mathematics 188 26 Density of Air (July 2009) 190 27 Bending Light (August 2009) 195 28 Saws and Modeling (November 2008) 201 29 PDEs of Fluids (September 2008) 207 30 Euler and Gravity (December 2009—A Guest Column by Dominic Klyve) 214 Part VI: Euleriana 222 31 Euler and the Hollow Earth: Fact or Fiction? (April 2007) 224 32 Fallible Euler (February 2008) 230 33 Euler and the Pirates (April 2009) 238 34 Euler as a Teacher – Part 1 (January 2010) 244 35 Euler as a Teacher – Part 2 (February 2010) 247 About the Author 252 'Read Euler, read Euler, he is master of us all' LaPlace exhorted us. And it is true, Euler writes with unerring grace and ease. He is exceptionally clear thinking and clear speaking. It is a joy and a pleasure to follow him. It is especially so with Ed Sandifer as your guide. Sandifer has been studying Euler for decades and is one of the world's leading experts on his work. This volume is the second collection of Sandifer's 'How Euler Did It' columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler's clever inventiveness and Sandifer's wonderful ability to explicate and put it all in context C. Edward Sandifer has been studying Euler for decades and is one of the world's leading experts on his work. This book is the second collection of Sandifer's 'How Euler Did It' columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician in history, this volume will leave the reader marveling at Euler's clever inventiveness, which Sandifer explicates and puts in context. The Final 35 How Euler Did It Columns Are All Collected In This Book. ... They Are Lightly Edited Versions Of The Columns As They Actually Appeared On Maa Online Between March 2007 And February 2010.--page Xiii. Pt. I. Geometry -- Pt. Ii. Number Theory -- Pt. Iii. Combinatorics -- Pt. Iv. Analysis -- Pt. V. Applied Mathematics -- Pt. Vi. Euleriana. C. Edward Sandifer, Western Connecticut State University. Includes Bibliographical References. "The final 35 How Euler Did It columns are all collected in this book. ... They are lightly edited versions of the columns as they actually appeared on MAA Online between March 2007 and February 2010"-- Page xiii