Math question

[HeyBub]

First you write the equation for the curve as a function of x: f(x) = equation.

Area = the integral [from 0 to max x] f(x)dx. Turning the crank gives the answer.

An alternative is the Monte Carlo method.

Surround the curve with a box. Generate random points that will land inside the box. Determine whether each generated point is inside the curve or outside. If 62% of the random points lie within the curve, the area of the curve is 62% of the area of the box. Obviously precision grows as a function of the sheer number of points.

[HeyBub]

There is no way to figure the area of an irregular, curved object using plane geometry.

[aemeijers]

4 bricks and some string to provide a reference rectangle around the pool, a large pad of graph paper (the 11x17 pads they sell at the art supply stores are great for this), a tape measure, and about an hour of time to sketch it out and count the squares. Some chalk to make witness marks along string path and at edge of pool so you don't lose track of where you are may be helpful. A framing square may be helpful to ensure square corners on the rectangle, and good measurements from string to pool edge. A kid to hold the other end of the tape while you make measurements would make it go faster.

Yes, all the calculus formulas can probably back into the same answer, but you would never be sure. For trivial problems, sometimes the stone-age methods are best.

[David Nebenzahl]

On 10/7/2009 4:21 PM SteveB spake thus:

42, of course.

(And it's a calculus question, not geometry.)

[Mike Paulsen]

Of course not. That's why we're using fancy geometry.

[blueman]

No problem - we all suffer from them - and the older we get, the more frequent they become, just like real gas ;)

[Red Green]

"SteveB" wrote in news:ql5vp6-60b2.ln1 @news.infowest.com:

After all this time you found a use for calculus! :-) But something tells me you don't have the equation for the perimeter. Just a hunch.

Let's say you were looking at a drawing of the perimeter. If you drew 9 vertical lines you would divide it into 10 approximate rectangles from which you could figure the approximate area (the ends of the rectangles are not really square of course) If you divided it into 100 it would be less approximate and 1000 even more accurate. At a billion-trillion divisions the unsquare ends of the rectangles become negligible. In calculus the number of divisions approaches infinity aka: limit as n approaches infinity.

BFD you say!

Start dividing up rectangles depending on how accurate you need it!

[Mike Paulsen]

1. Measure the perimeter. Write it down on a scrap of paper. Throw the paper away.
2. Find your pool on google earth or google maps satellite view.

1. Print it, being sure to include something in the print which is easy to measure. (deck, section of fencing, etc.)

2. Weigh the print.

1. Carefully cut out the pool. Weigh the pool

2. Using the actual length of the easy to measure object, determine the area represented by the entire print.

1. Fill in:

mass of pool cutout area of pool (unknown)

------------------- = -------------------- mass of entire print area of entire print

1. Do the math: (mass of pool) * (area of entire print) / (mass of entire print) = (area of pool)

[Red Green]

"HeyBub" wrote in news:uLadnbFyarTztVDXnZ2dnUVZ [e-mail]:

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.

[Red Green]

Mike Paulsen wrote in news:aQbzm.33634$As.8446 @newsfe13.iad:

lol

[Red Green]

Red Green wrote in news:Xns9C9DEDAD94BD6RedGreen@216.168.3.70:

p.s. One of the sections of the link that HeyBub posted has some basic graphics (pictures!) that show what I tried to put into words.

[mike]

Since the OP doesn't know the formula for the outline of the pool, he's going to have to stick with simple numerical methods.

See problem #6 in the following link. It shows an example.

You just have to remember to use and even number of "panels". Simpson's rule, properly done, will end up being more far more accurate for such a shape than your ability to read the measuring tape accurately.

[Red Green]

RicodJour wrote in news: [e-mail]:

Without the dot dot dots so the link works.

You're welcome! ;)

Little bit more on it.

You're welcome! ;)

[Red Green]

mike wrote in news: [e-mail]:

Oh my! Bonus points!! Happy happy, joy joy!

[Red Green]

"SteveB" wrote in news:ql5vp6-60b2.ln1 @news.infowest.com:

Looks like from all the replies you're gettin' too much info here Steve. Here's a simple solution.

Look at perimeter from a distance. Hold arm straight out with thumb up. Line up thumb with eye and shape. Pull number out of your ass...like maybe 42. Yer dun.

[SteveB]

Since the OP doesn't know the formula for the outline of the pool, he's going to have to stick with simple numerical methods.

See problem #6 in the following link. It shows an example.

You just have to remember to use and even number of "panels". Simpson's rule, properly done, will end up being more far more accurate for such a shape than your ability to read the measuring tape accurately.

reply: We do a lot of pools. Some are simple rectangles. Others are complex, but can be subdivided into geometric forms and simple math solves for those. It's just when I get one that looks like a blob that I have a problem. These are done from aerial photos, and once you blow it up so far, it starts to pixelate, and accurate measurements are no longer possible. I can get it pretty close with plain math.

Steve

[RicodJour]

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

[HeyBub]

Sorry, that's a completely different question. Five cents more, please.

[harry k]

I like it. Could use a string, stretch it carefully around the pool edge, measure length, solve for diameter of circle, solve for area.

Harry K

[DerbyDad03]

"plane geometry" is used to find the area of aircraft.