Math question - Page 4

Posted by blueman on October 7, 2009, 5:36 pm

> SteveB wrote:

>> How do I figure the area of a pool from the perimeter? It is a
>> kidney shaped (exaggerated) pool.
>> Steve

> How critical is the measurement? I would sketch out the length and
> width, cut off triangles for the belly of the kidney and outside the
> curves....area of the rectangle less the areas (roughly triangular)
> outside of the curves should give a fairly close measurement.

This is probably the best simple way if an approximation is OK.
You can get as precise as you want by making the sketch more precise
and projecting it on a fine grid and counting the "squares" and
fractions of "squares" covered by the pool.

Posted by SteveB on October 7, 2009, 7:20 pm

>> SteveB wrote:

>>> How do I figure the area of a pool from the perimeter? It is a
>>> kidney shaped (exaggerated) pool.
>>> Steve

>> How critical is the measurement? I would sketch out the length and
>> width, cut off triangles for the belly of the kidney and outside the
>> curves....area of the rectangle less the areas (roughly triangular)
>> outside of the curves should give a fairly close measurement.

> This is probably the best simple way if an approximation is OK.
> You can get as precise as you want by making the sketch more precise
> and projecting it on a fine grid and counting the "squares" and
> fractions of "squares" covered by the pool.

For my use, I took four widths, averaged them, then multiplied by the
length.

Close enough.

Steve

Posted by HeyBub on October 7, 2009, 4:04 pm

SteveB wrote:

> How do I figure the area of a pool from the perimeter? It is a kidney
> shaped (exaggerated) pool.

You can't. That's what Integral Calculus is for.

Posted by MikeB on October 7, 2009, 6:23 pm

> SteveB wrote:

> > How do I figure the area of a pool from the perimeter? =A0It is a kidne=

> > shaped (exaggerated) pool.

> You can't. That's what Integral Calculus is for.

So what is the formula then, or how would one use integral calculus to
derive the area of the pool?

Posted by HeyBub on October 7, 2009, 7:46 pm

MikeB wrote:

>> SteveB wrote:

>>> How do I figure the area of a pool from the perimeter? It is a
>>> kidney shaped (exaggerated) pool.

>> You can't. That's what Integral Calculus is for.

> So what is the formula then, or how would one use integral calculus to
> derive the area of the pool?

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.
http://hyperphysics.phy-astr.gsu.edu/Hbase/integ.html#c3

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.

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