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jazzfishBleh. 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.
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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.
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.
no subject
Date: 2009-07-16 12:32 am (UTC)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.
Date: 2009-07-16 01:16 pm (UTC)Re: don't harsh my mellow, man.
Date: 2009-07-16 11:28 pm (UTC)