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Curves for the Mathematically Curious
An Anthology of the Unpredictable, Historical, Beautiful, and Romantic
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Julian Havil
Language:
English
Published/Copyright:
2019
About this book
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.
Author / Editor information
Julian Havil is the author of John Napier: Life, Logarithms, and Legacy; The Irrationals: A Story of the Numbers You Can't Count On; Impossible? Surprising Solutions to Counterintuitive Conundrums; Nonplussed! Mathematical Proof of Implausible Ideas; and Gamma: Exploring Euler's Constant (all Princeton). He is a retired former master at Winchester College, England, where he taught mathematics for more than three decades.
Reviews
"Overall, the book was a delight to read. The writing is witty and entertaining, the history is at times peculiar and surprising, and the mathematics is rich and engaging. It would make a fine addition to a classroom bookcase or home coffee table, but while there are plenty of elegant diagrams and intriguing stories to give every curious reader the chance to glimpse mathematical beauty, only those with the ability to dig beneath the surface will understand just how much beauty this book has to offer."---Samuel Hewitt, Mathematical Gazette
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"Havil’s narrative for each curve is a cornucopia of fun facts and rigorous explanation."---Andrew J. Simoson, Mathematical Intelligencer
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"A wonderful addition to libraries where the mathematically curious find their reading."
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"What a beautiful book!"---Jonathan Shock, Mathemafrica.org
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"Undoubtedly [this book], written in the same entertaining unmistakable style of the author and containing a lot of information - mathematical, historical and general - will attract, as the previous ones, a large audience."---S. Cobzas, Studia Mathematica
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"This is not your father’s – or grandfather’s – standard collection of conic sections."---Jim Stein, New Books Network
Topics
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Frontmatter
i -
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Contents
ix -
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Preface
xiii -
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Acknowledgments
xvii -
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Chapter One. The Euler Spiral
1 -
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Chapter Two. The Weierstrass Curve
15 -
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Chapter Three. Bézier Curves
32 -
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Chapter Four.66 The Rectangular Hyperbola
50 -
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Chapter Five. The Quadratrix of Hippias
66 -
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Chapter Six. Two Space-Filling Curves
85 -
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Chapter Seven. Curves of Constant Width
104 -
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Chapter Eight. The Normal Curve
126 -
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Chapter Nine. The Catenary
155 -
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Chapter Ten. Elliptic Curves
183 -
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Perhaps the Most Important Curve of All
227 -
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Appendix A. The Title Page
229 -
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Appendix B. Conics Encapsulated
232 -
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Appendix C. A Trigonometric Variant for the Bézier Curve
234 -
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Appendix D. Envelopes
236 -
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Appendix E. The Mathematics of an Arch
240 -
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Appendix F. The Simple Pendulum
242 -
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Appendix G. Fibonacci’s Method
243 -
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References
247 -
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Index
255
Publishing information
Pages and Images/Illustrations in book
eBook published on:
October 21, 2019
eBook ISBN:
9780691197784
Pages and Images/Illustrations in book
eBook ISBN:
9780691197784
Keywords for this book
Logarithm; Elliptic curve; Mathematician; Mathematics; Result; Catenary; Hyperbola; Calculation; Normal distribution; Geometry; Summation; Mathematical optimization; Error; Parabola; Proportionality (mathematics); Hyperbolic function; Hilbert curve; Squaring the circle; Variable (mathematics); Parity (mathematics); Spline (mathematics); Series (mathematics); Mathematical analysis; Function (mathematics); Line segment; Number theory; Equation; Probability; Numerical integration; Reuleaux triangle; Sign (mathematics); Quadratrix; Gaussian function; Tunnell's theorem; Complex number; Conchoid (mathematics); Theorem; Diagram (category theory); Diameter; Arc (geometry); Polynomial; Curvature; Geometric progression; Curve of constant width; Pure mathematics; Fixed point (mathematics); Angle trisection; Differentiable function; Geometric mean; Inverse Galois problem; Modular arithmetic; Concatenation (mathematics); Riemann hypothesis; Quadratic equation; Addition; Inequality (mathematics); Disquisitiones Arithmeticae; Mathematical structure; Measurement; Curve fitting; Conjecture; Congruent number; Semicircle; Space-filling curve; Parametric equation; Conic section; Unit interval; Curve; Arithmetic; Arithmetic mean
Audience(s) for this book
For a non-specialist adult audience
