Facts about e

Some Facts about e

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
                     
```

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