Difference between revisions of "Bonnet net"
From Encyclopedia of Mathematics
(Importing text file) |
Ulf Rehmann (talk | contribs) m (tex encoded by computer) |
||
| Line 1: | Line 1: | ||
| + | <!-- | ||
| + | b0169001.png | ||
| + | $#A+1 = 2 n = 0 | ||
| + | $#C+1 = 2 : ~/encyclopedia/old_files/data/B016/B.0106900 Bonnet net | ||
| + | Automatically converted into TeX, above some diagnostics. | ||
| + | Please remove this comment and the {{TEX|auto}} line below, | ||
| + | if TeX found to be correct. | ||
| + | --> | ||
| + | |||
| + | {{TEX|auto}} | ||
| + | {{TEX|done}} | ||
| + | |||
An [[Isothermal net|isothermal net]] whose lines have constant geodesic curvature. The square of the line element in the parameters of this net is: | An [[Isothermal net|isothermal net]] whose lines have constant geodesic curvature. The square of the line element in the parameters of this net is: | ||
| − | + | $$ | |
| + | ds ^ {2} = | ||
| + | \frac{du ^ {2} +dv ^ {2} }{(U+V) ^ {2} } | ||
| + | , | ||
| + | $$ | ||
| − | where | + | where $ U = U(u), V = V(v) $. |
| + | Studied by O. Bonnet in 1848. | ||
Latest revision as of 10:59, 29 May 2020
An isothermal net whose lines have constant geodesic curvature. The square of the line element in the parameters of this net is:
$$ ds ^ {2} = \frac{du ^ {2} +dv ^ {2} }{(U+V) ^ {2} } , $$
where $ U = U(u), V = V(v) $. Studied by O. Bonnet in 1848.
How to Cite This Entry:
Bonnet net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bonnet_net&oldid=14588
Bonnet net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bonnet_net&oldid=14588
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article