Anharmonicity: Difference between revisions

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m Examples in physics: sp, date & link fixes; unlinking common words, replaced: Møller-Plesset → Møller–Plesset using AWB
 
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{{About|the concept in geometry|the concept in [[mathematical optimization]]|Fenchel's duality theorem}}
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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}}

Latest revision as of 01:25, 14 March 2014

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