Pedoe's inequality [SEP] named after
Pedoe's inequality
In geometry, Pedoe's inequality (also Neuberg–Pedoe inequality), named after Daniel Pedoe (1910–1998) and Joseph Jean Baptiste Neuberg (1840–1926), states that if "a", "b", and "c" are the lengths of the sides of a triangle with area "ƒ", and "A", "B", and "C" are the lengths of the sides of a triangle with area "F", then
with equality if and only if
Weitzenböck's inequality
In mathematics, Weitzenböck's inequality, named after Roland Weitzenböck, states that for a triangle of side lengths formula_1, formula_2, formula_3, and area formula_4, the following inequality holds:
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.
Geometric interpretation and proof.
Rewriting the inequality above allows for a more concrete geometric interpretation, which in turn provides an