Curves for the Mathematically Curious

An Anthology of the Unpredictable, Historical, Beautiful, and Romantic

Julian Havil

• Publisher: Princeton University Press
• Year: 2019
• Print ISBN:
  9780691206134
  9780691180052
• eBook ISBN:
  9780691197784
• Topic: Mathematics
• Subtopic: Art General
• Index: Mathematics

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.

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Contents
• Preface
• Acknowledgments
• CHAPTER ONE The Euler Spiral
• CHAPTER TWO The Weierstrass Curve
• CHAPTER THREE Bézier Curves
• CHAPTER FOUR The Rectangular Hyperbola
• CHAPTER FIVE The Quadratrix of Hippias
• CHAPTER SIX Two Space-Filling Curves
• CHAPTER SEVEN Curves of Constant Width
• CHAPTER EIGHT The Normal Curve
• CHAPTER NINE The Catenary
• CHAPTER TEN Elliptic Curves
• Perhaps the Most Important Curve of All
• Appendix A The Title Page
• Appendix B Conics Encapsulated
• Appendix C A Trigonometric Variant for the Bézier Curve
• Appendix D Envelopes
• Appendix E The Mathematics of an Arch
• Appendix F The Simple Pendulum
• Appendix G Fibonacci’s Method
• References
• Index