Math + CS = 11

In all of math, probability and statistics is the topic I hate. There’s just something about it that bugs me. Maybe it’s because I’ve never had a “good” teacher, but it’s most likely that it just doesn’t click with me. This quarter at RIT, I am lucky enough to take it and maybe I will learn exactly what I hate about it.

Since the classes last for 2 hours, most classes have a 5 to 10 minute break in the middle of them. During this break, I discovered something that I never knew about Pascal’s Triangle which I found really interesting. For those of you who don’t know Pascal’s triange here is the algorithim for making it.

1. The first row begins with 1
2. The second row has two 1’s, so: 1 1
3. Each additional row begins and ends with 1, and each number is the the sum of the two numbers that are above and in between it

Here’s a picture from mathforum.org!

Source: http://mathforum.org/

If you look at the first few rows, you might say to yourself, “Wow, those look like powers of 11!” I did at least. 1 = 11^0, 11 = 11^1, 121 = 11^2, 1331 = 11^3, and 14641 = 11^4. But what about 15101051? 11^5 = 161051, not 15101051. But what if we take each number in that row of Pascal’s Triangle as the number of 10’s, 100’s, 1000’s, and so on.

So, there should be one 1, five 10’s, ten 100’s, ten 1000’s, five 10000’s, and one 100000. If you do some conversion to base 10, you will have one 1, five 10’s, zero 100’s, one 1000’s, 6 10000’s, and one 100000. Writing this as a number, 161051 or 11^5.

The next row of Pascal’s Triangle, 1615201561 would be just 1771561 which is 11^6. The next row, 172135352171 would be 19487171 which is 11^7 and so on. More generalized, if you convert the nth row of Pascal’s Triangle to base 10, you can get the n-1th power of 11.

Ain’t that neat?