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e: The Story of a Number by Eli Maor

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15

But What Kind of Number Is It?

Number rules the universe.—MOTTO OF THE PYTHAGOREANS

The history of π goes back to ancient times; that of e spans only about four centuries. The number π originated with a problem in geometry: how to find the circumference and area of a circle. The origins of e are less clear; they seem to go back to the sixteenth century, when it was noticed that the expression (1 + 1/n)n appearing in the formula for compound interest tends to a certain limit—about 2.71828—as n increases. Thus e became the first number to be defined by a limiting process, e = lim(1 + 1/n)n as n → ∞. For a while the new number was regarded as a kind of curiosity; then Saint-Vincent’s successful quadrature of the hyperbola brought the logarithmic ...

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