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, as shown by Balitrand in 1916.
Statement of the inequality
Consider an acute triangle in the Euclidean plane with side lengths a, b and c and area A. Then
This inequality fails for general triangles (which was Ono's original conjecture), as shown by the counterexample a = 3/4, b = 1/2, c = 1.
- Balitrand, F. (1916). "Problem 4417". Intermed. Math. 23: 86–87.
- Ono, T. (1914). "Problem 4417". Intermed. Math. 21: 146.
- Quijano, G. (1915). "Problem 4417". Intermed. Math. 22: 66.