Maor E. The Story of a Number E

Princeton University Press, 1994. — 223 p.The story of pi has been told many times, both in scholarly works and in popular books. But its close relative, the number e, has fared less well. Despite the central role it plays in mathematics, its history has never before been written for a general audience. The present work fills this gap. Geared to the reader with only a modest background in mathematics, the book describes the story of e from a human as well as a mathematical perspective. In a sense, it is the story of an entire period in the history of mathematics, from the early 17th to the late 19th century, with the invention of calculus at its centre. Many of the players who took part in this story are brought to life. Among them are John Napier, the eccentric religious activist who invented logarithms and - unknowingly - came within a hair's breadth of discovering e; William Oughtred, the inventor of the slide rule; Newton and his bitter priority dispute with Leibniz over the invention of calculus, a conflict that impeded British mathematics for more than a century; and Jacob Bernoulli.John Napier, 1614
Recognition
Computing with Logarithms
Financial Matters
To the Limit, If It Exists
Some Curious Numbers Related to e
Forefathers of the Calculus
Prelude to Breakthrough
Indivisibles at Work
Squaring the Hyperbola
The Birth of a New Science
The Great Controversy
The Evolution of a Notation
e^x: The Function That Equals Its Own Derivative
The Parachutist
Can Perceptions Be Quantified?
e^θ: Spira Mirabilis
A Historic Meeting between J. S. Bach and Johann Bernoulli
The Logarithmic Spiral in Art and Nature
(e^x + e^-x)/2: The Hanging Chain
Remarkable Analogies
Some Interesting Formulas Involving e
e^ix: "The Most Famous of All Formulas"
A Curious Episode in the History of e
e^x+iy: The Imaginary Becomes Real
But What Kind of Number Is It?
Appendixes
Some Additional Remarks on Napier’s Logarithms
The Existence of lim(1 +1/n)ⁿ as n → ∞
A Heuristic Derivation of the Fundamental Theorem of Calculus
The Inverse Relation between lim (b^h-1)/h=1 and lim (1+h)^1/h=b as h → 0
An Alternative Definition of the Logarithmic Function
Two Properties of the Logarithmic Spiral
Interpretation of the Parameter φ the Hyperbolic Functions
e to One Hundred Decimal Places