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Topic: Curvature in Cartesian Plane
Replies: 6   Last Post: Nov 15, 2012 8:53 AM

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William Elliot

Posts: 1,449
Registered: 1/8/12
Re: Curvature in Cartesian Plane
Posted: Nov 15, 2012 5:28 AM
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On Thu, 15 Nov 2012, Brad Cooper wrote:
> "Mike Terry" <news.dead.person.stones@darjeeling.plus.com> wrote in message
> While investigating this I came across this in Spiegel's Vector Analysis:
>
> The radius of curvature rho of a plane curve with equation y = f(x),
> i.e. a curve in the xy plane is given by
>
> rho = sqrt(1+(y')^2) / |y''|
>

No, rho = (1 + y'^2)^(3/2) / |y"|

> I tested this with the simple hemisphere y = sqrt(1-x^2).

That's a semicircle.



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