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设欧氏平面上△iiiABC三边长为iiiabc,面积为(1,2)iiD=.Neuberg曾提出如下一个猜想: 222222111()Habca+-+22222111()bcab+- 2222211112()16cabc++-DD, (1) 等号成立当且仅当△111ABC∽△222ABC. D.Pedoe率先证明了不等式(1)成立[1],不等式(1)即为著名的Neuberg-Pedoe不等式.?
Suppose the three sides of ΔiiiABC on the Euclidean plane are iiiabc and the area is (1,2) iiD=. Neuberg has proposed the following conjecture: 222222111()Habca+-+22222111()bcab+- 2222211112()16cabc++-DD, (1 The equal sign is established if and only if Δ111ABC∽Δ222ABC. D.Pedoe first proved that inequality (1) holds [1] and inequality (1) is the famous Neuberg-Pedoe inequality.