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Index
Cover page
Halftitle page
Frontispiece
Title page
Copyright page
Preface
Contents
Other
Introduction
The most beautiful theorem in mathematics
Euler, his equation, and his identity
Chapter 1: 1
The counting numbers
Number systems
Number names
Chapter 2: 0
The nothingness number
Much ado about nothing
Calculating with zero and negative numbers
From integers to real numbers
Chapter 3: π
The circle number
Why π ?
Early values
Using polygons
Radian measure
Infinite expressions
Arctan formulas
A miscellany of results
Some weird results
Enter the computer
Measuring the Earth
Chapter 4: e
The exponential number
Polynomial and exponential growth
Introducing logarithms
Enter the calculus
A problem of interest
Properties of e
Hanging chains and derangements
Exponential growth and decay
Chapter 5: i
The imaginary number
Different types of numbers
Solving equations
The origins of i
Picturing complex numbers
Generalizing complex numbers
Chapter 6: eiπ+1 = 0
Euler’s equation
Two near misses
Euler’s identity
Some consequences
What are ln i, ii, and ?
Who discovered Euler’s equation?
Further Reading
Image credits
Publisher’s Acknowledgements
Index
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