Math question - Page 5

Posted by Red Green on October 7, 2009, 11:31 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.

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.

>
> 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.
>
>

Posted by HeyBub on October 8, 2009, 7:29 am

Red Green wrote:

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

> 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.

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

Posted by Red Green on October 8, 2009, 9:23 pm

> Red Green wrote:

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

>> 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.

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

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'?

Posted by David Combs on November 2, 2009, 1:06 am

>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.

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.

>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.

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

Posted by Jon Danniken on October 7, 2009, 4:12 pm

SteveB wrote:

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

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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