WOLFRAM|DEMONSTRATIONS PROJECT

Hadwiger-Finsler Inequality

​
2
AB
+
2
BC
+
2
CA
≃ 445.6800
AB-BC
2
)\),
+BC-CA
2
)\),
+CA-AB
2
)\),
+4
3
area[ABC] ≃ 428.937
For a triangle with side lengths
a
,
b
,
c
, and area
A
, the Hadwiger–Finsler inequality states that
2
a
+
2
b
+
2
c
≥
2
(a-b)
+
2
(b-c)
+
2
(c-a)
+4
3
A
, with equality holding if and only if the triangle is equilateral.