• Leonard Euler first used e in 1736 to mean "that number whose hyperbolic logarithm is equal to 1."
  • e is sometimes called "Euler's number."

  • In 1737, Euler first used the symbol for pi to be the ratio of the circumference to the diameter in a circle.
  • In 1777, Euler first used i to be equal to the square root of -1.

  • And Euler was the first to write e^(pi * i) + 1 = 0,
    which contains the five most significant numbers in all of mathematics. 
  •    
        1    1    1    1    1
e = 1 + -- + -- + -- + -- + -- + ...
        1!   2!   3!   4!   5!
  • e is defined as the limit as n approaches infinity of (1 + 1/n) ^ n.
  • So e = 2.718281828459045 ...

  • e can also be defined as the limit as n approaches zero of (1 + n) ^ (1/n).
  • e is the base of the exponential function y=a^x such that the slope of the tangent to the curve at the point (0,1) is 1. -- Bill Turner

  • You can remember this approximation for e by recalling some facts about Andrew Jackson.
    • He was elected twice as President of the U.S.
    • He was the seventh President of the U.S.
    • He was first elected in 1828.
    • Since he served two terms, write down another 1828.
    • He was a general in the War of 1812 and won the battle of New Orleans. He wore a pair of 45s on his hips, and 45 + 45 = 90. So the next 6 digits are 459045.

  • Some mnemonics for e:
    • It enables a numskull to memorize a quantity of numerals. -- Gene Widhoff

    • To express e, remember to memorize a sentence to simplify this. -- John L. Greene

    • I'm forming a mnemonic to remember a function in analysis. -- Maxey Brooke

    • It repeats: A constant of calculus,
                      A constant of calculus.
                      -- Jeffrey Strehlow

    • A French riddle to remember the digits of "e" :

      Tu aideras a rappeler ta quantite a beaucoup de docteurs amis.
      (You will help to remember your quantity to many friend doctors.)