For the practical use of Calculus

How do you figure out the function of a particular curve of a real-life object that isn't a circle or something simple like that?

What if I had an elliptical-shaped wing that isn't a perfect ellipse? How do I find the wing area of that object? I know I can "cheat" and just break up the wing into smaller trapezoids, but that's not what I'm here for.

I've always wondered about how people figure out the function of the curve of some real-life object.

You don't.  There's not a function you could write out on paper that parametrizes the shape of an airplane wing.  In practice you'd have a CAD model or something similar of the wing, which approximates the structure with a polygonal mesh.  You could easily compute the volume/surface area/etc. of this model on the computer, but it's not something you could do by hand.

>>2
So if I gave you an object that is straight on 3 sides, and curvy on the other. There would be no way to figure out the function of the curvy side (broken into parts or not)?

>>3
Well yeah, if you break it into parts you can approximate it as close as you like by a piecewise linear function.  There's not a general way to find a function that parametrizes an arbitrary curvy line; there are infinitely many curved shapes and only so many elementary functions.

>>4
>>2
What the fuck is wrong with you faggots? Just use a power series.

>>5
You're a dumbass.  If I give you an airplane wing and ask you to find a function parametrizing it's shape how exactly do you propose to "use a power series?"

>>6
*its

http://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem

>>8
That gives EXISTENCE of polynomial approximations to continuous functions, not a way to find them.  You can construct them if you already know what the original function is, for example using Taylor series.  If I give you an arbitrary curve you can't use the Stone-Weierstrass theorem to find a polynomial that fits it; you would need to use a computer to find some interpolating curve.  That curve would NOT be just a truncated power series; if you try to use high order polynomials for practical interpolation, you run into major problems; see http://en.wikipedia.org/wiki/Runge%27s_phenomenon.

>>9
I never said anything about finding polynomial approximations, only that they exist.  I didn't mention Taylor series because there are convergence problems for functions like 1/(1+x^2) due to the poles at +-i (among the reasons why, as you said, we don't always use truncated power series).

Runge's phenomenon only means you run into problems if you use equally spaced interpolation points.  Randomly chosen interpolation points usually gets around this problem.

As for actually attempting a polynomial interpolation,
http://en.wikipedia.org/wiki/Lagrange_polynomial

vandermonde matrices up in this shit

lol applied math.

OP, I hope this shows that approxmiation using Riemman sums is best.

More like, I Want a Pedo Pal!

>>15
Are you an troll!