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Hadwiger-Finsler inequality (Theorem)

In a triangle with sides $ a$, $ b$, $ c$ and an area $ A$ the following inequality holds:

$\displaystyle a^2+b^2+c^2\geq (a-b)^2+(b-c)^2+(c-a)^2 +4A\sqrt{3}.$



"Hadwiger-Finsler inequality" is owned by mathwizard.
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See Also: Weizenbock's inequality


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proof of Hadwiger-Finsler inequality (Proof) by mathwizard
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Cross-references: inequality, area, sides, triangle
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This is version 2 of Hadwiger-Finsler inequality, born on 2002-06-06, modified 2002-12-26.
Object id is 3061, canonical name is HadwigerFinslerInequality.
Accessed 4021 times total.

Classification:
AMS MSC: 51M16 (Geometry :: Real and complex geometry :: Inequalities and extremum problems)
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