Anharmonicity: Difference between revisions
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{{About|the concept in geometry|the concept in [[mathematical optimization]]|Fenchel's duality theorem}} | |||
In [[differential geometry]], '''Fenchel's theorem''' ([[Werner Fenchel]], 1929) states that the average [[curvature]] of any closed convex plane curve is | |||
: <math> \frac{2 \pi}{P},</math> | |||
where ''P'' is the perimeter. More generally, for an arbitrary closed curve in space the average curvature is <math>\ge \frac{2 \pi}{P}</math> with equality holding only for convex plane curves. | |||
==References== | |||
* W. Fenchel, Über Krümmung und Windung geschlossener Raumkurven, Math. Ann. 101 (1929), 238-252. [http://www.springerlink.com/content/v45m1546747t2315/] | |||
[[Category:Theorems in differential geometry]] | |||
{{differential-geometry-stub}} | |||
Revision as of 01:16, 14 January 2014
29 yr old Orthopaedic Surgeon Grippo from Saint-Paul, spends time with interests including model railways, top property developers in singapore developers in singapore and dolls. Finished a cruise ship experience that included passing by Runic Stones and Church.
In differential geometry, Fenchel's theorem (Werner Fenchel, 1929) states that the average curvature of any closed convex plane curve is
where P is the perimeter. More generally, for an arbitrary closed curve in space the average curvature is with equality holding only for convex plane curves.
References
- W. Fenchel, Über Krümmung und Windung geschlossener Raumkurven, Math. Ann. 101 (1929), 238-252. [1]