E (mathematical constant)

The mathematical constant e is the base of the natural logarithm function. Its value to the 29th decimal digit is:

History

The first references to the constant were published in 1618 in the table of an appendix of a work on logarithms by John Napier. However, this did not contain the constant itself, but simply a list of natural logarithms calculated from the constant. It is assumed that the table was written by William Oughtred. The first indication of e as a constant was discovered by Jacob Bernoulli, trying to find the value of the following expression.

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: lim_{n oinfty} left(1+rac{1}{n} ight)^n

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The first known use of the constant, represented by the letter b, was in correspondence from Gottfried Leibniz to Christiaan Huygens in 1690 and 1691. Leonhard Euler started to use the letter e for the constant in 1727, and the first use of e in a publication was Euler's Mechanica (1736). While in the subsequent years some researchers used the letter c, e was more common and eventually became the standard.

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The exact reasons for the use of the letter e are unknown, but it may be because it is the first letter of the word exponential. Another possibility is that Euler used it because it was the first vowel after a, which he was already using for another number, but his reason for using vowels is unknown. It is unlikely that Euler choose the letter because it is his first initial, since he was a very modest man, always trying to give proper credit to the work of others.

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Mathematical constant: A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. Unlike physical constants, mathematical constants are defined independently of any physical measurement....

Natural logarithm: The natural logarithm, invented by John Napier, is the logarithm to the base e, where e is equal to 2.71828... (continuing forever as e is irrational, like π). The natural logarithm is defined for all positive real numbers x and can also be defined for non-zero complex numbers as will be explaine...

William Oughtred: William Oughtred (March 5, 1575 – June 30, 1660) was an English mathematician....

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