设△A1B1C1和△A2B2C2的三边长分别为a1、b1、c1和a2、b2、c2,面积分别为△1、△2,则H≡a22(b21+c21-a21)+b22(c21+a21-b21)+c22(a21+b21-c21)≥16△1△2,(1)当且仅当△A1B1C1∽△A2B2C2时等号成立.1891年,J.Neuberg首先提出了不等式(1),1942年,D.Pedoe重新发现并第一个给出了证明,该不等式实际上是利用△1和△2给出了H的一个下界估计.1991年,杨世国先生在文[1]中 Assuming that the three sides of △ A1B1C1 and △ A2B2C2 are a1, b1, c1 and a2, b2 and c2, respectively, the area is Δ1 and Δ2 respectively, then H≡a22 (b21 + c21- a21) + b22 (1) If and only if △ A1B1C1∽ △ A2B2C2, the equality sign holds. In 1891, J.Neuberg first proposed inequalities (1), In 1942, D.Pedoe rediscovered and first proved that this inequality actually gives a lower bound estimate of H using Δ1 and Δ2. In 1991, Mr. Yang Shiguo in [1]