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Re: Urgent Help needed

  • To: mathgroup at
  • Subject: [mg20419] Re: [mg20390] Urgent Help needed
  • From: "Andrzej Kozlowski" <andrzej at>
  • Date: Tue, 26 Oct 1999 00:33:04 -0400
  • Sender: owner-wri-mathgroup at

The equation F(x,y,z) = 0 does not define a curve but a surface in R^3 (the
level surface corresponding to c). Since curvature is a local invariant
there is no general formula that determines the curvature (Gaussian, mean
etc)at any point of a arbitrary surface given in this way  you need local
coordinates or patches i.e. parametric equations).

Andrzej Kozlowski
Toyama International University

>From: "Vladimir Tsyrlin" <vtsyrlin at>
To: mathgroup at
>To: mathgroup at
>Subject: [mg20419] [mg20390] Urgent Help needed
>Date: Mon, Oct 18, 1999, 15:40

> Given the implcit form of a curve, i.e. F(x,y,z) = 0, do you know how to
> find the curvature of F at a point in 3D space? All the references I have
> assume F is in parametric form and take the standard differential geometry
> approach.
> --
> **************************************************
> *************Vladimir Tsyrlin *******************
>  vtsyrlin at   vtsyrlin at
> ******************************************************

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