2.71828183: The Number e Song

Two point seven one eight two eight one eight three
is approximately the value of the constant "e".
The sum for n ranging from nought to infinity,
of 1 on n factorial is e.

With compound interest, the more frequently
the compounding's performed you'll watch your balance grow to e.
As the number of periods approaches infinity
the limit of (one plus (one on n)) all to the n is e.

Two point seven one eight two eight one eight three
is approximately the value of the constant "e".
It's one of five constants in The Identity
e to the (i pi) plus one is zero, you'll see:

Complex exponentiation links trigonometry
with algebra, coz when you raise the magic number e
to the i x, it's cos(x) plus an imaginary
component with value sin(x), Euler said with glee!

Two point seven one eight two eight blah blah is "e".
The function e to the x is its own derivative.
The natural logarithm is log to the base e.
e's irrational, its digits don't repeat
periodically, they continue infinitely
and are probably distributed uniformly.
Two point seven one eight three.

Download a high-quality version of the video (about 6MB) (requires Xvid codec)
Download the MP3 (about 2.5MB)

Apologies to any digit-memorisers out there! (I do say "approximately equal to"...)

Email: fmatrix at danielwedge dot com
Feel free to play this in lectures etc, you have my permission (though I'd be interested to hear from you if you do!)

Daniel Wedge
1 August 2010