"that's not math, it's got numbers in it."

[jazzfish]

Bleh. The time I was going to spend writing things for LJ last week turned into work, and the parts that weren't work were a detailed mathy analysis of the ruby strategy in Scepter of Zavandor (because I needed to chew on something decidedly left-brain-y). Which means I failed to mention Wednesday gaming, Sunday brunch and housewarming, or Tuesday dinner and conversation.

Not that I've much to say about any of those. Other than that spending time with a few good people is Good, in almost exactly the way that spending time with lots of people I don't know well isn't.

---

Via Dr rivka, A Mathematician's Lament (warning: PDF), in which I discover that I should have been a mathematician.

To wit: on page 3 or 4, there's a picture of a triangle inside a rectangle, and the question: "how much of the rectangle does the triangle take up?" I looked at it for like five seconds and said "oh, that's easy, you just run a perpendicular line from the top of the triangle to the base, and you've got two rectangles, each half filled with a triangle. So the whole triangle takes up half the area of the whole box." Which, yeah, he goes on to explain that. Then a page later he rails against the fact that kids aren't taught that that process of discovery and problem-solving is math. Instead, math is plugging numbers into "A = 1/2*b*h".

And I got it. I understood, conceptually, why that's the area of a triangle, in a way I never had before. And it is simple and elegant and beautiful, and it took my breath away.

I love things like that. The moment of perfect clarity when something just makes sense, when the bits of a problem come together and fall into place. It's. . . euphoric. It's spellbinding in the same way the Ansel Adams exhibit had me transfixed, with the added bonus of: I did that.

Not that I had any idea that that was what math was really about. Sure, I read Martin Gardner and Douglas Hofstadter, and was on "the math team" in eighth grade, but. . . that was fun. Math was algebra and calculus and diffy-q, problem set after problem set and painstaking attention to every minute detail. Exactly the kind of thing I can't stand.

But, still. A triangle is half the size of the rectangle it fits into. Gorgeous.

Comments

[pictsy.livejournal.com]

I think I should have been a mathematician too. It was my one true love until Mr. Sabo crushed my soul. Maybe I'll start again.

[jazzfish]

I don't even know where one /would/ start. (Also, there's that whole "time" thing.)

And, yeesh, Sabo. I was lucky enough to dodge him, and had only mediocre math teachers instead of the genuinely bad ones. (Doc Stallings excepted, of course.)

[pictsy.livejournal.com]

Once in a while I think about reteaching myself math until I get to the point that I need help, and then taking classes at Nova or GMU. I don't know if I'd want a degree, or how many degrees I would want. After reading the whole Lament, though, maybe I should start with all the math history and appreciation material that never came up in school.

And thats why I like theory over practice

[stormking.livejournal.com]

Theory of math is filled with those nifty things and seeing how it's all related. pratice of math is hoping you remembered to carry the 5.

[thanate.livejournal.com]

I'm awful at the super-basic stuff and the calculus & beyond. The bits in the middle, which require thinking rather than memorization, and equations you can re-deduce by examining the problem (and therefore that I don't have to memorize...) always worked well for me.

The problem with being a mathematician in this day and age is that all the easy/interesting stuff has already been worked out, and you are left with increasingly complex abstractions. My mother, who was a math major in college (mainly so that her children's lit class would count towards graduation, I kid you not) would have made an excellent engineer, whereas my father, from whom I got my appalling lack of mathematical clerical ability, was an engineering major but would have made a better abstract mathematician.

[jameshroberts.livejournal.com]

A triangle is half the size of the rectangle it fits into.

Clarification. A triangle whose base is the length of one side of the rectangle, and whose other vertex touches the opposite side of the rectangle is half the size of that rectangle. That's the example shown in the article.

You could stick in a triangle whose corners just touch three sides of the rectangle and it would be less than half the area of that rectangle.

I guess you could say in general, a triangle is at most half the size of the rectangle it fits into. But I'm far too lazy to work out a proof of that.

don't harsh my mellow, man.

[jazzfish]

Smallest rectangle it fits into, then. This formulation also lets us dodge the awkward situation where one of the base angles is obtuse.

Re: don't harsh my mellow, man.

[jameshroberts.livejournal.com]

Sorry, I can't help myself when it comes to this stuff. But I hadn't even thought about the obtuse problem. You're right of course. That was an acute observation. Thank you, I'll be here all week. Try the veal.

[nixve.livejournal.com]

I dunno, personally I loved algebra. Calculus, trig and all the rest felt horrible and like a chore to do. But algebra, I loved solving for "y", I'd do pages of it just for fun. I know I'm weird.

[ndkid.livejournal.com]

For me, physics classes were the only place where I ever saw higher math get cool. The only example that comes to mind offhand: terminal velocity. *Why* is there terminal velocity? Here were were, happily dealing with 9.8 m/s^2, and all the fun math that pops out of that, and, WHAM! Now, all of a sudden, that's just not enough anymore... that 9.8 m/s^2 actually slows down the faster you're going.

So how do we solve all that? Watch, as calculus handily walks onto the screen!
(I will also forever hold a special place in my heart for the nifty beauty that is Fourier Transforms...)