Monday, February 20, 2012

Confessions of a Math Geek

I love calculus.

If there's anything that cements and seals my "I'm a Geek" badge, that statement is it. And I'm okay with that.

Do you know what you can do with calculus? I've found most people who never took calculus have no idea what it involves, so here are some highlights.

You can find the slope of curves. Remember slope? You learned about it in algebra, probably with some variety of "rise-over-run." It tells you how steep a straight line is, the rate at which it increases or decreases.

Well, with calculus, you can find that rate at a specific point on a curvy line. It's starts off a little ugly and scary, with a formula that looks like this (or a variation on it):

After laboring through several problems with this not-so-fun process, your teacher reveals that there are ridiculously easy shortcuts.

You want to kill your teacher. (I warn my students ahead of time that this will happen.) Then you get over it and get to work.

This may not sound that useful, but think about all the things that involve rates. Velocity, acceleration, how quickly something is growing or shrinking, etc.

Later on, you learn how to find the area under curves. Again, it starts with a slightly complex process that you soon simplify (until it gets harder again). This concept extends to taking the graph of an equation, imagining that you're spinning it around an axis, and finding the volume of that 3-D shape.

There are ways this is useful, too. But from the time I learned it, I thought it was just insanely cool all by itself.

Yup. A geek, for sure.

You know what's even stranger? That slope-finding process and the area-finding process turn out to be inverses of each other. Totally unexpected, but it's part of what makes it easier in the long run.

Anyone else have a topic they learned about in school that just makes them geek out to an irrational degree? A certain period in history, or a concept in science? It's safe to share. All geeks are welcome here.


S L Jenan said...

QCD is my guilty geek pleasure - Yes, lovely quantum chromodynamics. If my MS can't be about quarks and gluons, I don't want to write it.

Did you know that 98.8% of the mass of any proton is merely binding energy (via e=mc^2) between the three quarks that it contains? So of my 171 lbs, 169 lbs are nothing but energy relationships. I'm only two pounds of stuff-- the rest is just magic.

Revo said...

I learned if I parked next to the dumpster right outside my sixth period class, I could be the first guy out of the parking lot.
It is a skill that I've used repeatedly in my every day life.

Also, if you dare a guy enough, you can get him to take a hit off a bunsen burner. Swear him to silence or the school nurse will be quite irked.

R.C. Lewis said...

SL, very cool! :)

Revo ... I don't even know what to say. :-P