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ozone

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## Homework Statement

We are given a function defined by

[itex] x = uv,

y = 1/2 (u^2-v^2)[/itex]

## Homework Equations

I derived the line element [itex] ds^2 = (u^2+v^2) dv^2 + (u^2+v^2) du^2 [/itex]

However I decided this was to unwieldy to derive our circumference where

C = [itex]2*{R}\oint_{-R}^{R} ds[/itex]

So I decided to try to convert my coordinats to polar. I realized the equation of a 2-d circle in these coordinates is

[itex] 4(y^2+x^2) = (u^2+v^2) = R^2[/itex]

so then R = 2r in polar coordinates.. right? I think I can use this information to construct a simple integral in polar coordinates but i don't know exactly what to do.

Thanks in advance

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