Radius of Curvature: Formula & Name

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SUMMARY

The formula for computing the radius of curvature at a point on a surface is given by \(\frac{1}{\rho_c}=\frac{\partial G/\partial S}{2\sqrt{E}G}\), where \(E\) and \(G\) are the first fundamental coefficients and \(S\) is the arc length parameter. This formula computes the principal curvature, specifically related to Gauss curvature. The discussion clarifies that the formula is indeed associated with Gauss curvature, confirming its relevance in differential geometry.

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manushanker20
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I am working on a paper that provides the following formula for computing radius of curvature at a point on a surface.

\frac{1}{\rho_c}=\frac{\partial G/\partial S}{2\sqrt{E}G}

where E,G are first fundamental coefficients and S is the arc length parameter.

Can anyone please tell me the name of the curvature the above mentioned formula computes.
 
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