Weitzenböck's inequality

In mathematics, Weitzenböck's inequality, named after Roland Weitzenböck, states that for a triangle of side lengths ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, and area ${\displaystyle \Delta }$, the following inequality holds:

${\displaystyle a^{2}+b^{2}+c^{2}\geq 4{\sqrt {3}}\,\Delta .}$

Equality occurs if and only if the triangle is equilateral. Pedoe's inequality is a generalization of Weitzenböck's inequality. The Hadwiger–Finsler inequality is a strengthened version of Weitzenböck's inequality.