Inegalitatea Finsler-Hadwiger pentru tetraedru
Posted: Thu Nov 29, 2007 1:51 pm
Sa se arate ca in orice tetraedru \( A_{1}A_{2}A_{3}A_{4} \) de muchii \( a_{1}, a_{2}, \ldots , a_{6} \) are loc inegalitatea:
\( \sum_{i=1}^{6} a_{i}^{2}\geq 12\sqrt[3]{9}V^{2/3}+\frac{1}{3}\sum_{1\leq i<j \leq 6} (a_{i}-a_{j})^{2} \).
\( \sum_{i=1}^{6} a_{i}^{2}\geq 12\sqrt[3]{9}V^{2/3}+\frac{1}{3}\sum_{1\leq i<j \leq 6} (a_{i}-a_{j})^{2} \).