A most elegant equation : Euler's formula and the beauty of mathematics

A most elegant equation Euler's formula and the beauty of mathematics

David Stipp

Book - 2017

"Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The re...sult is an ode to this magical field." -- Amazon.com.

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Subjects
Euler, Leonhard, > 1707-1783.
Euler's numbers.
Numbers, Complex.
Mathematics > History.
Published
New York : Basic Books [2017]
Language
English
Main Author
David Stipp (author)
Edition
First edition
Physical Description
viii, 221 pages : illustrations ; 22 cm
Bibliography
Includes bibliographical references (pages 193-199) and index.
ISBN
9780465093779
  • Introduction
  • 1. God's Equation
  • 2. A Constant That's All About Change
  • 3. It Even Comes Down the Chimney
  • 4. The Number Between Being and Not-Being
  • 5. Portrait of the Master
  • 6. Through the Wormhole
  • 7. From Triangles to Seesaws
  • 8. Reggie's Problem
  • 9. Putting It Together
  • 10. A New Spin on Euler's Formula
  • 11. The Meaning of It All
  • Appendix 1. Euler's Original Derivation
  • Appendix 2. Why i i Is Real
  • Acknowledgments
  • Glossary
  • Bibliography
  • Notes
  • Index
Review by Choice Review

Two of the most famous equations in mathematics are Euler's formula and the Pythagorean theorem. This work focuses on Euler's formula, or "God's equation," and eloquently explores its profound and timeless beauty. Stipp, an accomplished science writer, begins with a background understanding of the formula's key constants--e, i, pi, 0, and 1--and an introduction to the prolific 18th-century mathematician for whom the equation is named. Stipp then offers a more detailed exploration of the proof for Euler's formula, guiding readers step by step to a nuanced understanding of its implications and touching on concepts in trigonometry, infinite sums, complex numbers, vectors, and infinity in the process. The text also places the formula in the context of other mathematicians' work, such as that of Abraham de Moivre. After a brief mention of an application of Euler's formula, Stipp concludes with a compelling discussion of the formula's connections to concepts of beauty. The book contains a useful glossary and chapter notes. Accessible to anyone willing to wade through some well-presented mathematics, this book is suited to a broad audience; the wider world would benefit from understanding how a mathematical formula can be beautiful. Summing Up: Recommended. All readers. --Jerry Johnson, emeritus, Western Washington University

Copyright American Library Association, used with permission.

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