Euler formula

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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).


See also Normal curvature; Principal curvature.


[a1] M. do Carmo, "Differential geometry of curves and surfaces" , Prentice-Hall (1976)
[a2] W. Blaschke, K. Leichtweiss, "Elementare Differentialgeometrie" , Springer (1973)
How to Cite This Entry:
Euler formula. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article