Curves for the Mathematically Curious : An Anthology of the Unpredictable, Historical, Beautiful, and Romantic

A biographical sketch of ten curves – how they came to be, their importance in the past, and their continuing relevance today. **Ten amazing curves personally selected by one of today's most important math writers** __Curves for the Mathematically Curious__ is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of a curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bézier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves—and now you can share in this adventure. __Curves for the Mathematically Curious__ is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling. Ten amazing curves personally selected by one of today's most important math writers Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bézier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves—and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling. "Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of a curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bézier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves--and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling."--Publisher's description Cover......Page 1 Curves forthe Mathematically CuriousAN ANTHOLOGY OF THEUNPREDICTABLE, HISTORICAL,BEAUTIFUL AND ROMANTIC......Page 5 Copyright......Page 6 Dedication......Page 7 Contents......Page 11 Preface......Page 15 Acknowledgments......Page 19 1 The Euler Spiral......Page 23 2 The Weierstrass Curve......Page 37 3 Bézier Curves......Page 54 4 The Rectangular Hyperbola......Page 72 5 The Quadratrix of Hippias......Page 88 6 Two Space-Filling Curves......Page 107 7 Curves of Constant Width......Page 126 8 The Normal Curve......Page 148 9 The Catenary......Page 177 10 Elliptic Curves......Page 205 Perhaps the Most Important Curve of All......Page 249 Appendix A. The Title Page......Page 251 Appendix B. Conics Encapsulated......Page 254 Appendix C.A Trigonometric Variant for the Bézier Curve......Page 256 Appendix D.Envelopes......Page 258 Appendix E.The Mathematics of an Arch......Page 262 Appendix F.The Simple Pendulum......Page 264 Appendix G.Fibonacci’s Method......Page 265 References......Page 269 Index......Page 277