Pedoe's inequality

Today it means: The observation 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 another triangle with area F, then A²(b²+c²-a²)+B²(a²+c²-b²)+C²(a²+b²-c²)≥16Ff,, with equality if and only if the two triangles are similar with pairs of corresponding sides (A, a), (B, b), and (C, c). Full definition →