1983年,笔者曾在大学毕业论文中证得 定理 设x,y,z∈R~+,则在△ABC和△A′B′C′中,有式中等号当且仅当△ABC∽△A′B′C′且x:sin2A=y:sin2B=z:sin2C时成立. 在通用符号下,①式可变形或特殊化为 其中λ,μ,u∈R~+.由①～⑤式可推出外森比克不等式、费-哈不等式、高灵不等式、纽贝格-匹多不等式及一系列结果,这些在文[1]、[2]、[3]中曾作过讨论。下面再给出几个新的结果。 In 1983, the author had established the theorem for x, y, z ∈ R + + in the graduation thesis of the university. In △ABC and △A′B′C′, there was a formula with a medium sign if and only if △ABC ∽ △ A’B’C’ and x:sin2A=y:sin2B=z:sin2C holds. Under the general symbol, 1 can be deformed or specialised as λ,μ,u∈R~+. From 1 to 5 Can be introduced in the Senbisuke inequality, Fei-Hag inequality, Gao Ling inequality, Nuoberg-Pittot inequality and a series of results, which are discussed in [1], [2], [3]. Here are some new results.