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Trigonometric Delights

  • Eli Maor
Language: English
Published/Copyright: 2013
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Volume 67 | Princeton Science Library

About this book

A fun, entertaining exploration of the ideas and people behind the growth of trigonometry

Trigonometry has a reputation as a dry, difficult branch of mathematics, a glorified form of geometry complicated by tedious computation. In Trigonometric Delights, Eli Maor dispels this view. Rejecting the usual descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. From the proto-trigonometry of the Egyptian pyramid builders and the first true trigonometry developed by Greek astronomers, to the epicycles and hypocycles of the toy Spirograph, Maor presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social growth. A tapestry of stories, curiosities, insights, and illustrations, Trigonometric Delights irrevocably changes how we see this essential mathematical discipline.

Author / Editor information

Eli Maor is a former professor of the history of mathematics at Loyola University Chicago. His books include the internationally acclaimed To Infinity and Beyond, e: The Story of a Number, The Pythagorean Theorem: A 4,000-Year History, and Music by the Numbers (all Princeton).

Reviews

"This book is full of interesting historical accounts about the development of mathematics."—Richard S. Kitchen, Mathematics Teacher

"Trigonometric Delights should be required reading for everyone who teaches trigonometry and can be highly recommended for anyone who uses it."—George H. Swift, American Mathematics Monthly

"If you always wanted to know where trigonometry came from, and what it's good for, you'll find plenty here to enlighten you."—Ian Stewart, New Scientist

"[Maor] writes enthusiastically and engagingly. . . . Delightful reading from cover to cover."—Sean Bradley, MAA Online

Topics

  • Publicly Available

    Frontmatter

    i
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  • Publicly Available

    Contents

    vii
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  • Publicly Available

    Preface

    xi
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    PROLOGUE. Ahmes the Scribe, 1650 B.C.

    1
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    Recreational Mathematics in Ancient Egypt

    11
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    1. Angles

    15
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    2. Chords

    20
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    Plimpton 322: The Earliest Trigonometric Table?

    30
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    3. Six Functions Come of Age

    35
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    Johann Müller, alias Reginunutanus

    41
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    4. Trigonometry Becomes Analytic

    50
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    Franςois Viete

    56
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    5. Measuring Heaven and Earth

    63
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    Abraham De Moivre

    80
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    6. Two Theorems from Geometry

    87
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    7. Epicycloids and Hypocycloids

    95
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    Maria Agnesi and Her "Witch"

    108
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    8. Variations on a Theme by Gauss

    112
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    9. Had Zeno Only Known This!

    117
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    10. (sinx)/x

    129
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    11. A Remarkable Formula

    139
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    Jules Lissajous and His Figures

    145
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    12. tanx

    150
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    13. A Mapmaker's Paradise

    165
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    14. sin x = 2: Imaginary Trigonometry

    181
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    Edmund Landau: The Master Rigorist

    192
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    15. Fourier's Theorem

    198
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    Appendixes

    211
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    Bibliography

    225
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    Credits for Illustrations

    229
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    Index

    231

Publishing information
Pages and Images/Illustrations in book
eBook published on:
April 7, 2020
eBook ISBN:
9780691202204
Pages and Images/Illustrations in book
Main content:
256
Other:
107 b/w illus.
https://doi.org/10.1515/9780691202204
eBook ISBN: 9780691202204
Keywords for this book
Trigonometry; Mathematics; Trigonometric functions; Theorem; Equation; Mathematician; Regiomontanus; Summation; Complex number; Circumference; Geometry; Cartesian coordinate system; Fourier series; Geometric progression; Fourier; Pythagorean theorem; Astronomy; Result; Rectangle; Astroid; Radian; Bessel function; Line segment; Quantity; Map projection; Right triangle; Al-Battani; Quadratic equation; Mercator projection; Pure mathematics; Diameter; Unit circle; Logarithm; Sine; Scientific notation; Just intonation; Stereographic projection; Abraham de Moivre; Series (mathematics); Hypocycloid; Muhammad ibn Musa al-Khwarizmi; Real number; Periodic function; Roger Cotes; Hyperbola; Power series; Florian Cajori; Euler's formula; Isaac Barrow; Epicycloid; Notation; Nathaniel Bowditch; Abstract algebra; Number theory; Polynomial; Spherical trigonometry; 61 Cygni; M. C. Escher; Calculation; Natural logarithm; Textbook; Floor and ceiling functions; Metric system; Liber Abaci; Nicolaus Copernicus; Asger Aaboe; Circle of latitude; Zeno's paradoxes; Descartes' rule of signs; Christopher Clavius; Significant figures; Big O notation; Richard Courant; Squaring the circle; Gemma Frisius; Infinitesimal; Trigonometric tables; Spherical Earth; Georg von Peuerbach; Infinite product; Figure of the Earth; Coefficient; Fibonacci; Bertrand Russell; Theodolite; Sign (mathematics); Sexagesimal; Line (geometry); Numerical integration; Elementary function; Men of Mathematics; Scientist; Pythagorean triple; Blaise Pascal; Accuracy and precision; Gnomon; Partial fraction decomposition; Eric Temple Bell; Dirichlet integral; Daniel Bernoulli
Audience(s) for this book
General/trade;Professional and scholarly;College/higher education;
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