Euler formula for normal curvature
= Euler formula for normal curvature
{c}
{title2=$\kappa_n=\kappa_1\cos^2\theta+\kappa_2\sin^2\theta$}
If a unit tangent makes angle $\theta$ with the first principal direction, the <normal curvature> is $\kappa_n=\kappa_1\cos^2\theta+\kappa_2\sin^2\theta$. This follows by diagonalizing the <second fundamental form> relative to the <first fundamental form>. When the <Gaussian curvature> is nonnegative, $|\kappa_n|\leq2|H|$.