Re: multivariable calculus question

[[Mr.] Lynn Kurtz]

On Sat, 15 Dec 2007 10:50:45 -0800 (PST), gaga
<baroness...@gmail.com> wrote:

>would you be able to explain to me how to parametrize the curve?
>
>thank you
>:)

Would you be able to include enough context so those of us who just
tuned in know what the hell you are talking about?

--Lynn

[Virgil]

In article
<982b4f4f-4c2c-48c6...@e4g2000hsg.googlegroups.com>,
gaga <baroness...@gmail.com> wrote:

> would you be able to explain to me how to parametrize the curve?
>
> thank you
> :)

What "curve"?

[David C. Ullrich]

On Sat, 15 Dec 2007 10:50:45 -0800 (PST), gaga
<baroness...@gmail.com> wrote:

>would you be able to explain to me how to parametrize the curve?

No problem: x = x(t), y = y(t).

Or, in a way that's more formally correct,

x = f(t), y = g(t).

>thank you
>:)

************************

David C. Ullrich

[G.E. Ivey]

First, get a curve!

Seriously, there are many different ways to parameterize a curve. In fact a single curve can have many different parameterizations. If, in 2 dimensions, you have a curve given by y= f(x) then x= t, y= f(t) works nicely. Sometimes you can identify a geometric property that can be used as parameter: In a circle, center at the origin, radius R, if we measure the angle theta counter-clockwise from the positive x axis, then from basic trig, the x-coordinate of a point is x= Rcos(theta) and the y-coordinate is y= Rsin(theta). Those are perfectly good parametric equations for the circle.

Often we can think of an object MOVING along a curve with some speed. We can think of x(t), y(t), z(t) as the coordinates of the point at time t. You would need to pick a "starting" point, x(0), y(0), z(0) and a speed function v(t) to make that precise. Finally, a "natural" parameterization for a curve is to use arc-length. Choose some starting point (and a "positive" direction and label each point x(s), y(s), z(s) where s is the distance measured along the curve from (x0,y0,z0) to (x,y,z), s positive in the "positive" direction, negative in the opposite direction.

In sum, how you find a parameterization for a curve depends strongly not only on what the curve itself is, but upon what you want to do with it. If you have a particular problem you are working on,post and we will try to help.

[Frederick Williams]

"David C. Ullrich" wrote:
>
> On Sat, 15 Dec 2007 10:50:45 -0800 (PST), gaga
> <baroness...@gmail.com> wrote:
>
> >would you be able to explain to me how to parametrize the curve?
>
> No problem: x = x(t), y = y(t).
>
> Or, in a way that's more formally correct,
>
> x = f(t), y = g(t).

That won't do. Gaga's curve is in R^3. I know he didn't say so, but
since you're a professional mathematician you should have known it
anyway.

--
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