Hadwiger-Finsler inequality

The inequality of Hadwiger Finsler (after Hugo Hadwiger and Paul Finsler ) is an elementary geometric statement about triangles. It says that for every triangle with sides a , b and c and area F the following inequality applies:

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

The inequality of Weitzenböck results from this immediately as a corollary .

literature

• Paul Finsler, Hugo Hadwiger: Some Relations in the Triangle . In: Commentarii Mathematici Helvetici , 10, No. 1, 1937, pp. 316-326. doi: 10.1007 / BF01214300
• Claudi Alsina, Roger B. Nelsen: When Less is More: Visualizing Basic Inequalities . MAA, 2009, ISBN 978-0-88385-342-9 , pp. 84-86

Web links

• Hadwiger-Finsler inequality . In: PlanetMath . (English)