A formula expressing the normal curvature of a surface in a given direction $l$ in terms of the principal curvatures $k_1$ and $k_2$:
where $\phi$ is the angle between the direction $l$ and the principal direction corresponding to the principal curvature $k_1$.
This formula was established by L. Euler (1760).
|[a1]||M. do Carmo, "Differential geometry of curves and surfaces" , Prentice-Hall (1976)|
|[a2]||W. Blaschke, K. Leichtweiss, "Elementare Differentialgeometrie" , Springer (1973)|
Euler formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_formula&oldid=32596