Euler formula
From Encyclopedia of Mathematics
A formula expressing the normal curvature of a surface in a given direction 
in terms of the principal curvatures 
and 
:
 |
where 
is the angle between the direction 
and the principal direction corresponding to the principal curvature 
.
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