Math question

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2 ways --
1. If you have a good GPS unit, create a GPS track around the pool. The GPS will have the algorithms to calculate the area.
2. Drain the pool. Determine the average depth. Calibrate the rate of fill (time a garden hose to fill a measured container - 1 gal, 5 gal, or something similar. Refill the pool, timing the refill. The timing tells you how many gallons or how many cu. ft, depending on how you calibrated it. Now you know the volume and can work back to the area.
Actually, I like the "draw it out on a piece of graph paper and count the squares" method.
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A GPS that will count that short a distance, and calculate an area as small as 500 square feet? I want one!
Steve
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wrote:

It may be pedestrian model. Best suited for city slickers. These can help navigate short distances and home in shorter distances.
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John H. Holliday wrote:

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

Of course not. That's why we're using fancy geometry.
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lol
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"plane geometry" is used to find the area of aircraft.
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That's baaaddd.
Harry K
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SteveB wrote:

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.
--
aem sends....

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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!
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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.
http://hyperphysics.phy-astr.gsu.edu/Hbase/integ.html#c4
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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.
http://tinyurl.com/y9cphfy
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.
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wrote:

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

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.
http://tinyurl.com/y9cphfy
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
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SteveB wrote:

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.
3. Print it, being sure to include something in the print which is easy to measure. (deck, section of fencing, etc.)
4. Weigh the print.
5. Carefully cut out the pool. Weigh the pool
6. Using the actual length of the easy to measure object, determine the area represented by the entire print.
7. Fill in:
mass of pool cutout area of pool (unknown) ------------------- = -------------------- mass of entire print area of entire print
8. Do the math: (mass of pool) * (area of entire print) / (mass of entire print) = (area of pool)
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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
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That would give only an upper limit to the area. The greater the deviation of the shape from circular, the greater the deviation of the computed area from the actual area.
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On Oct 8, 10:01am, snipped-for-privacy@milmac.com (Doug Miller) wrote:

True, I overlooked that. My solution wouldn't even come close.
Harry K
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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
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Mike Paulsen wrote:

It is an exact answer.
My exact answer is pour 55 gallons of motor oil in the pool (perhaps 0W20).
The oil, of course, floats. Measure the thickness of the oil layer. Since you know the thickness and the volume, determining the area is trivial.
--
bud--

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