Ono's inequality
In mathematics, Ono's inequality is a theorem about triangles in the Euclidean plane. In its original form, as conjectured by T. Ono in 1914, the inequality is actually false; however, the statement is true for acute triangles and right triangles, as shown by F. Balitrand in 1916.Consider an acute or right triangle in the Euclidean plane with side lengths a, b and c and area A. Then
This inequality fails for general triangles, as shown by the counterexample
The inequality holds with equality in the case of an equilateral triangle, in which up to similarity we have sides and area
