Ten amazing curves personally selected by one of today's most important math writersCurves 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.

• Cover
• Title
• Copyright
• Dedication
• Contents
• Preface
• Acknowledgments
• CHAPTER ONE The Euler Spiral
  • 1.1 An Unusual Parametrization…
  • 1.2 …Yet a Natural Parametrization
  • 1.3 A Challenge
  • 1.4 One Curve, Many Names
• CHAPTER TWO The Weierstrass Curve
  • 2.1 Naive Thoughts
  • 2.2 Profound Thoughts
  • 2.3 Differentiability
  • 2.4 Weierstrass’s Proof
  • 2.5 The Aftermath
  • 2.6 Final Thoughts
• CHAPTER THREE Bézier Curves
  • 3.1 Bézier’s Curve of Curves
  • 3.2 Bézier and Bernstein
  • 3.3 Bézier and Casteljau
  • 3.4 The Story of Lump
  • 3.5 The Story of O
• CHAPTER FOUR The Rectangular Hyperbola
  • 4.1 Old Logarithms
  • 4.2 A Thorny Problem
  • 4.3 Computation
  • 4.4 New Logarithms
• CHAPTER FIVE The Quadratrix of Hippias
  • 5.1 Problems of Antiquity
  • 5.2 Some Greek Constructions
  • 5.3 The Quadratrix and Trisection
  • 5.4 The Quadratrix and Circle Squaring
• CHAPTER SIX Two Space-Filling Curves
  • 6.1 Je Le Vois, Mais Je Ne Le Crois Pas
  • 6.2 Peano’s Function
  • 6.3 Hilbert’s Curve
  • 6.4 Peano’s Curve
• CHAPTER SEVEN Curves of Constant Width
  • 7.1 The Reuleaux Triangle …
  • 7.2 …And Its Generalizations
  • 7.3 And Their Generalization …
  • 7.4 A Circle in All but Name?
• CHAPTER EIGHT The Normal Curve
  • 8.1 A Fruitful Question
  • 8.2 An Answer but Not a Solution
  • 8.3 Approximating the Impossible
  • 8.4 Error Curves
  • 8.5 The Error Curve
  • 8.6 The Normal Distribution
• CHAPTER NINE The Catenary
  • 9.1 A Matter of Symmetry
  • 9.2 Historical Errors
  • 9.3 The Curve Identified
  • 9.4 Hyperbolic Functions
  • 9.5 The Chain Inverted
  • 9.6 A Bumpy Road
• CHAPTER TEN Elliptic Curves
  • 10.1 Elliptic Ambiguity
  • 10.2 Problems, Problems, Problems
  • 10.3 Common Ground
  • 10.4 The Congruent Number Problem
  • 10.5 An Arithmetic
  • 10.6 Fertile Fields
  • 10.7 Cryptography
  • 10.8 Apologia
• 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