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Math Question #1
8-bit
mudcub
Can anyone tell me what this equation means?

Equation

Thanks!

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(Deleted comment)
i did! 4 times! I got a C the first time, a D the 2nd time, an F the 3rd time, and dropped it on the no penalty drop day the 4th time.

so, what is it?

thank you for reminding me i got a D- in calculus.
ummm...
derivatives for radii and angles and something or other as poopoo caca doodywokka approaches 2pi?

I once tool a grad school class where on the first day, the professor said, "Now, just integrate around the unit circle..." and I knew I was in trouble and dropped the class the next day!

Normally, I'm pretty good at math, and enjoy it a lot. I *think* this equation is calculating the circumference of a circle, ellipse, or irregular object in polar coordinates, but I was wondering if this was a common equation, and what it was used for.

Here is the song that inspired this post... it's by the comedy troupe "Hard 'N Phirm", and it reminded me of the Kate Bush song:

http://www.patrickkellogg.com/Pi.mp3

i know and love the song - i'm a fan of Keith Schofield, who directed the video.

Whatever it is, you can use it to hack the Gibson.

Only if you hack a bank machine in, like, Bumsville, Idaho.

Took calc with an A...
But still am unsure what this is.
I'm venturing that it is the formula for a circumference of a circle given radius r.

But if r is constant, why bother integrating?

(Deleted comment)
I've used integration to find total area under graphs, especially between two x-coordinates. However the lack of coordinate data has me scratching my head. It is still something circumferential, I do maintain, but it looks unexessarily complicated to be "C = πd."

(Deleted comment)
Well, I just emailed it to my hubby, the chemical engineer/math geek. I got a headache just looking at it. It reminded me why I took several years of geometry.

Where did you find it?

It was on a CD by the comedy group "Hard 'N Phirm"... see the first post in the thread

If r is a polar function r = f(theta) then the arc length (the length of the curve) is given by the integral you have.

So, would C be circumference then?

Well circumference is specifically the full arc length of a circle... The formula you have is for any curve that you can write in the form r=f(theta). Think of anything ever drawn by a spirograph... This formula would let you calculate how long the curve is, that is, how far the pen would have travelled. As always, finding the function can be the hardest part!

[I'm rusty, but can one get a clue to the function by evaluting the integral at it's limits, maybe?]

This is correct.

If r is constant, dr/dΘ is 0, and the integral evaluates as πr^2 -- the circumference of a circle. This makes sense since the curve would be a circle if r is constant.

If r is not constant, then you have some other shape being described, and C is the length of the curve. You can think of it as the length an ant would walk if it followed the line of the graph of (r, f(Θ)).

Since we evaulate from 0 to 2*pi, that's a complete revolution, right? That's why I'm saying the formula was supposed to describe the circumference of a circular (or circular-like) object. Thanks to everyone who helped me puzzle this out!

Yes, "42" - the "hard way", as they say in craps.


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