It’s The Eleventh Eleventy-Eleven Today

As I’m sure you are all well aware, today is November 11, 2011. Or for those of us who might be number geeks, or like to see patterns in everything, 11/11/11. Truth be told, someone might have been so excited about today, that the moment the clock struck 11:11 and 11 seconds, someone might have planned to celebrate in his office with a delicious piece of chocolate.

Of course, because someone was instead attending Remembrance Day services, someone didn’t actually witness this event. So instead, I celebrated post 11:11 and 11 seconds on the 11th day of the 11th month in the 2011th year, but still with a delicious piece of chocolate. Actually 3 pieces. Because why celebrate with one piece when you can celebrate with three?

Honestly, I’ll celebrate anything to justify having chocolate. Not that I need to justify it. I am an adult after all. Or at least, if one were to slice me open and count my rings, that’s what my age would suggest.

But I digress.

Since it is 11/11/11, I thought I’d provide you with a little bit of number fun. Specifically, Pascal’s Triangle.

What is Pascal’s Triangle? It’s a simple triangle of numbers, built with very simple rules. First, you start with the number 1. Underneath the first 1 you write two 1s, such they form a triangle. On the next line you can imagine that there’d be 3 numbers, such that the previous two lines and the third form a larger triangle. The numbers start and end with 1, but the centre value is replaced with the sum of the two digits above it. The fourth line would have four numbers, again with a 1 in the first and last position. The central 2 positions would be replaced with the sum of the two digits above.

It’s probably best to see this in practice:

For example, on the line which reads 1, 6, 15, 20, 15, 6, 1, you’ll see that the 6=1+5, 15=5+10, 20=10+10, etc. These are the sums of the elements in the triangle above the positions of the 1, 6, 15, 20, etc. Simple, right?

Now here’s where the 11 stuff comes in. Each line represents (among other things), the powers of 11. That is, line 1 is $11^{0}=1$. Line 2 is $11^{1}=11$. Clearly $11^{2}=121$, $11^{3}=1331$, and so on. Of course, once you hit $11^{5}$ we have to account for the larger digits. But it’s really just a matter of adding up the right amount of 1s, 10s, 100s, 1000s, etc. In the case of the 6th line, we’d have

$11^{5}=1*1+5*10+10*100+10*1000+5*10000+1*100000=1+50+1000+10000+50000+100000= 161051$.

Cool stuff.

Anyway, I hope you enjoyed this 11th day of the 11th month of the 2011th year.