Difference between revisions of "Euler formula"
From Encyclopedia of Mathematics
(Importing text file) |
(TeX) |
||
| Line 1: | Line 1: | ||
| − | A formula expressing the normal curvature of a surface in a given direction | + | {{TEX|done}} |
| + | A formula expressing the normal curvature of a surface in a given direction $l$ in terms of the principal curvatures $k_1$ and $k_2$: | ||
| − | + | $$k_l=k_1\cos^2\phi+k_2\sin^2\phi,$$ | |
| − | where | + | 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). | This formula was established by L. Euler (1760). | ||
Latest revision as of 17:23, 30 July 2014
A formula expressing the normal curvature of a surface in a given direction $l$ in terms of the principal curvatures $k_1$ and $k_2$:
$$k_l=k_1\cos^2\phi+k_2\sin^2\phi,$$
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).
Comments
See also Normal curvature; Principal curvature.
References
| [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: http://encyclopediaofmath.org/index.php?title=Euler_formula&oldid=13608
Euler formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_formula&oldid=13608
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article