Math - My Journey with Choose

In light of recent stormy/controversial political events, why not take a break with something that everyone loves? (Or hates, but how could you possibly hate it?)

Math!

Yes, math. Ever since undergrad, I'd always fancied myself something of a math enthusiast. I don't understand half the stuff, but it's endless fascinating.

Lately, I've been going at a random college textbook I have. College Algebra and Trigonometry (from 1984 no less!) has a nice spread of concepts, including the mystifying sigma notation and the methods for doing matrix operations. Important today, however, is an equation found on the inside cover:

AKA binomial equation, or binomial formula

My interest was piqued when a math channel, associated with my favorite math(s) channel, Numberphile, did a video on the "choose function," which used the above equation to figure out the number of ways objects in a subgroup could be arranged in the overall group.

That same mathematician talked about how spreadsheets could be great fun, so I decided to combine the ideas. Doodling various combinations of 7 choose 2, or 7 choose 5, I saw that some results were the same. For instance, there are 7 ways to choose 1 object in 7 objects, and there is the same number of ways to choose 6 objects in the same group of 7.

Confused? It'll be cleared up soon, don't worry.

Figuring out a general equation proved to be too difficult/require too much effort, so I leaved off doing that. However, observing that the numbers increased and decreased in a steady manner, I did the only logical thing: I made a bar graph from the data. Witness the beauty below:

Extra large for your viewing pleasure

If you do any work with statistics at all, you'll recognized this as the normal distribution. I could go on about how the choose function is related to binomial coefficients and Pascal's triangle, but that would be excessive and redundant, since they're all so closely related.

With my limited skills in mathematics, being able to put things together like this was really fun. For the skilled mathematician, something like this is a given. It is fascinating to be able to take a series of numbers, work some "magic" with them in a spreadsheet, and discover a relation I never knew before.

But I suppose that's the heart of math, then? Using the tools to discover new and cool things?

Anyway, I'll close before I ramble on too long.