# Although I’m More Than e Weeks Late, Happy e-Day To All

I can’t believe I missed it.  Just over $e$ weeks ago, mathematicians, statisticians, physicists and other nerds celebrated a very important day; one of the math-i-est of math-y days.  And I missed it.  Missed it!  Gah!

That day was $e$-day.  “What is $e$-day?”, you ask?  Well, it’s only the celebration of Euler‘s1 constant, represented by the lowercase letter $e$.  Specifically

$e=\displaystyle{\sum_{n=0}^{\infty}}\frac{1}{n!}=1+\frac{1}{2}+\frac{1}{6}+\frac{1}{24}+\ldots\approx 2.71828183\ldots$

Notice how the first two digits have been used to identify the date on which this awesome number is to be celebrated.  Two decimal seven, or February 7.  This year.  Last year.  Every year.  The date that I completely forgot.  Gah!  If I were in Mathemagical class at Hogwarts, Gryffindor would have just lost about $e$ million points2.  Sigh.

Anyway, $e$ is a rather important number in the world of mathematics.  Like $\pi$, it is ubiquitous, appearing even when least expected.  Probably the most bizarre place is in the famous equation

$e^{i\pi}-1=0$.

This particular equation (a.k.a. Euler’s Identity) is rather interesting, at least to math-y type people, given that it combines the multiplicative constant 1, the additive constant 0, the complex (a.k.a. imaginary) unit $i$, Euler’s constant $e$, and my favourite constant $\pi$ into one tidy package.  Math is awesome.

Euler also gave us the exponential function $e^{x}$, which can be written as follows:

$e^{x}=\displaystyle{\sum_{n=0}^{\infty}}\frac{x^n}{n!}.$

And of course, we all know that this is the function whose derivative is itself.  Crazy stuff.  Finally, Euler also gave us the following formula

$e^{i\theta}=\cos{(\theta)}+i\sin{(\theta)},$

which can be used to generate Euler’s Identity (set $\theta=\pi$ and watch the magic happen).

So much awesome in one little constant.

On a fun note, check out this site.  You can determine where in the first 27, 182, 818 base 27 digits of $e$ you can find your name.

• Dan appears 1358 times; the first occurrence starting at position 7066.
• Euler appears only twice; the first occurrence at position 18260334.
• Math appears 43 times; the first occurrence starting at position 125764.
• Pi appears 37535 times; the first occurrence starting at position 443.

1 Pronounced in English as Oiler.  Just like Oiler in the Edmonton Oilers. I know, I can’t believe I just dropped a hockey reference either.

2 Yes, I assume I would be part of Gryffindor, thank you for asking. And it has nothing to do with the fact that I’m now sporting a Harry Potter lightning scar on my forehead.

3 You can find this word cloud here.

1. Rick says:

What the hell is hockey?

2. Beth says:

Rick! Bite your tongue! Hockey is only the greatest game ever in the history of ever! Oh wait, you live in Calgary – I can see why you wouldn’t know what hockey is – your team doesn’t even know how to play it.

In other news, “Beth” appears in e 50 times, with the first occurrence starting at position 792654. Also, I am only the 5th person to search for “Beth” on that site. What is wrong with you, other Beths out there? (Other than the 4 who have searched it. You 4 Beths are A-OK).

1. dangillis says:

Clearly all other Beths, apart from those that have already searched, are sub-par Beths. They should be referred to as beths, not Beths.