Math question

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wrote:

Little snag here. Has no idea what the equation is. Oh, but there's an area of mathematics for this too...after differential calculus and after integral calculus. Crank up the differential equations...mathematical equations for an unknown functions.

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Red Green wrote:

Sorry, that's a completely different question. Five cents more, please.
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Hmmm, let's see...[digging way down in corners of pocket] a screw, pocket lint, handy box knockout, reminder note that went through the wash...errr, how's my credit lookin'?
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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
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SteveB wrote:

You can estimate the area by overlaying the circumference of a couple of circles, figuring the area of each, then adding those areas together. Take the remaining area not covered by your circles, and estimate that area, adding it to the previous area to obtain your final rough estimate.
Jon
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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
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If accuracy is important, I'd use the Simpson's Rule formula, where you take measurements across the pool at interals and plug those distances into the formula. You also have to plug the interval distance into the formula.
Why do you ask?
http://tinyurl.com/y9h7av5
The hard part is Googling a web page that presents the formula in an easy to understand manner for novices.
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Found something. See problem #6 in the following link. It shows an example without too much math jargon
http://tinyurl.com/y9cphfy
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On 10/7/2009 1:18 PM mike spake thus:

Ackshooly, that's called "Simpson's approximation", but yes, it does work as you described. It's a weighted-average method of approximating the area under a curve.
--
Found--the gene that causes belief in genetic determinism

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http://en.wikipedia.org/wiki/Simpson's_rule
I never argue with Wikipedia when it agrees with me.
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David Nebenzahl wrote:

And, as delta-x approaches zero, you get the integral.
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Use SketchUp. It's probably the easiest way. http://edublog.sedck12.org/.../Calculating_Area_Irregular_Shapes.pdf
You're welcome! ;)
R
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wrote:

Without the dot dot dots so the link works.
http://edublog.sedck12.org/media/blogs/training/docs/Calculating_Area_Irregular_Shapes.pdf
You're welcome! ;)
Little bit more on it.
http://edublog.sedck12.org/media/blogs/iteam/CalcAreaIrregShapes.pdf
You're welcome! ;)
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Indeed I am. ;)
I did a "copy link location" since it was a PDF - first time I ever had an ellipsis swapped in there when I pasted. Remind me to proofread before I post next time. Thanks in advance!
I'm curious, does anyone else here use Sketchup for determining areas? I find it amazingly helpful when estimating. It's tailor made for such things as SteveB is doing. Only a few measurements are needed and then the curve is tweaked by eye.
R
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Here's a picture of what I'm talking about. I drew four curves - drew one curve of one end of the pool, copied it and moved the copy to the far end of the pool, scaled it to reverse its direction, and drew two curves tangent to the ends of the end curves. Then right clicked on the surface and chose the area function. It took me longer to write this than to draw it.
http://tinypic.com/r/35bvx2g/4
R
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wrote:

Looks pretty slick. Probably worth a few hours of investment time to learn to use if you have repeated uses as Steve says he does. If it only takes a few hrs to learn a specific use that speeds thing up, the ROI would be great.
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Agree
If designing in 3D no need to use ACAD any more anyway. Get a solids modeler like Solid Works
The ONLY thing I would use CADA for now days is 2D electrical schematics..... and I'm not even sure I would use ACAD in THAT case!
I spent 12 years using ACAD and will never go back to that again!
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Actually it's a geometry question...
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And the answer is ...................?
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On 10/7/2009 4:21 PM SteveB spake thus:

>>

42, of course.
(And it's a calculus question, not geometry.)
--
Found--the gene that causes belief in genetic determinism

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