Math question

[blueman]

Well the pool presumably have additives which may act as buffers so not so easy unless you know the exact chemical composition of the pool "water".

[zxcvbob]

Kidney shaped. Do you just *want* people to pee in the pool? (the power of suggestion)

Bob

[David Combs]

The old joke. Country yokel's son goes off to college.

Back at xmas vacation. "Well, son, what'd they teach you at college?"

"Pi r^2"

"Sure am wasting my money sending you off -- everyone with any sense knows that pie are square!"

Has anyone NOT heard that one?

David

[David Combs]

^^^^^^ round

Only I could screw that one up! :-)

David

[David Combs]

Learned this once (and yes, it has a name that I don't remember):

For symmetrical even if then leaned over -- something like that, sphere, cone, etc:

Volume = area of top + 4 * area of middle (cross section, I guess) + area of bottom, all divided by 6.

David

[David Combs]

Wrong. It isn't a "function" -- for every x, there's TWO y's.

Maybe somehow bisect the top of the pool, symmetrically. Or not symettrically.

NOW you have TWO SEPARATE curves, each doable (unless it's *really* weirdly shaped, parallel nooks and crannies(sp?)) via a y = f(x).

Integrating, you'll get two areas, to add together.

Long time ago, before computers, they had these mechanical complicated-linkage based things ("planeaometer"? something like that?), at the end of which was a tracing-needle or a pencil, etc, and when you traced around the curve, somehow you could read the area off some dial.

Fancy stuff out there before (digital) computers.

They had tide-predictors that emulated the fourier series that worked for that particular point (30 miles up the coast it might be very different series).

Of course (well, maybe not "of course") the Norden bombsight was totally (I think) mechanical, via gears, cams, linkages, etc (I guess -- I think it's still classified).

David

[David Combs]

Circles, triangles, etc. Maybe just triangles.

That's what they've been doing since the beginning of computer graphics, for "filling" closed curves with colors, say.

Stupidly, I forget the generic term for computing a set of triangles to, to some approximation, "fill" an area.

And to figure an approaching-optimum set of triangles, ie the FEWEST number of them (differently sized, of course) to fill an area. Triangles REALLY easy to compute, so easy that long ago they designed chips to do it "in hardware", REALLY quickly.

A picture might contain a jillion triangles, so doing them fast is important. Especially if you're doing it "in real time", ie like in an animation.

Not that I've ever done any of this stuff, nor even taken a class in it. But I am a mamber of ACM "SigGraph", and once a year get this heavy book of the yearly "proceedings" -- man, you have to be a physicist to do some of that stuff, and you want to see applications of REALLY hairy math,' and REALLY clever algorithms, you'll see them there.

Again, not that I actually understand it all, but I can at least read *parts* of *most* (well, many) of the included "papers". Nifty stuff indeed!

Oh, there's a newsgroup that's related: comp.graphics.algorithms, where I sometimes ask (my usual stupid) questions.

David

[David Combs]

How about one of those pencil-like things with a wheel on the end, and you wheel it around the perimeter (on the photo), and read off the perimeter directly. (Plus converting some units.)

David

[Harry K]

You _almost_ got it. Pi R Square...No pi are not square, cake are square, pi are round.

Harry K

[jeff_wisnia]

Lim time!

Said a rather dense yokel named Pete, "Mathematics has fair got me beat. I thought a square root, Is some sort of fruit, And Pi is a nice thing to eat."

Jeff

[Sam E]

Cornbread are square :-)

[blueman]

Your formula is certainly in general FALSE since volume is

3-dimensional and grows to first order as the cube of some notion of "radius" while your formula is just a weighted sum of 3 cross-sections.

Volume is volume. Area is area. Irregular shapes don't in general have nice formulas and require numerical approximation/integration.