E: The Story of A Number - Eli Maor (USA Princeton University Press, 1998)
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 seventeenth to the late nineteenth century, with the invention of calculus at its center. Many of the players who took part in this story are here 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, who lived a frugal and unhealthful life and died at the age of 86, reportedly of joy when hearing of the restoration of King Charles II to the throne of England; Newton and his bitter priority dispute with Leibniz over the invention of the calculus, a conflict that impeded British mathematics for more than a century; and Jacob Bernoulli, who asked that a logarithmic spiral be engraved on his tombstone - but a linear spiral was engraved instead! The unifying theme throughout the book is the idea that a single number can tie together so many different aspects of mathematics - from the law of compound interest to the shape of a hanging chain, from the area under a hyperbola to Euler's famous formula e[superscript i[pi]] = -1, from the inner structure of a nautilus shell to Bach's equal-tempered scale and to the art of M.C. Escher. The book ends with an account of the discovery of transcendental numbers, an event that paved the way for Cantor's revolutionary ideas about infinity. No knowledge of calculus is assumed, and the few places where calculus is used are fully explained.
App. 6. Two Properties of the Logarithmic Spiral -- App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions -- App. 8. e to One Hundred Decimal Places.
Keywords: Natural Sciences (3GdYdhe GdHMJIs; e (The number); General