# Changes

## Ellipsoid in three-dimensional Euclidean space

, 02:01, 6 August 2011
Fundamental forms and curvatures
| $e,f,g$ for [[second fundamental form]] using this parametrization || {{fillin}} || {{fillin}}
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| [[principal curvature]]s using this parametrization || eigenvalues of the [[shape operator, which is the matrix $\begin{pmatrix} E & F \\ F & G \\\end{pmatrix}$ ]] || {{fillin}}
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| [[mean curvature]] || arithmetic mean of the principal curvatures = half the trace of the shape operator = $(E + G)/2$ || {{fillin}}
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| [[Gaussian curvature]] || product of the principal curvatures = determinant of shape operator = $EG - F^2$ || {{fillin}}
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