Weitjenbock不等式证明的再探究

Exploration on the Demonstration of Weitjenbock Inequality

Weitjenbock不等式是一个典型的用代数方法证明几何不等式,自从1919年几何学家Weitjenbock给出这个著名的不等式并于1961年选为第三届国际奥林匹克试题,近百年来在数学界引起了极大的研究热情并给出了许多不同的证明方法。论文给出Weitjenbock不等式的5种多向思维新的证明方法,用三角的方法给出Finsler加强结果的一个新证明,进一步给出Weitjenbock不等式发散的几个新的证明。

Weitjenbock inequality is a typical geometric inequality of algebraic method to prove. Since 1919, the famous inequality was given by Weitjenbock, and it was chosen as the Third International Olympic Games in 1961. In the last hundred years, it has aroused great enthusiasm in the field of mathematics and gave a lot of different methods to prove it. The main purpose of this paper is to use the elementary method o propose some new different methods on the proof of Weitjenbock inequality in muti-direction thinking and to put forward a new mean over the proof of Finler strengthen result. Furthmore, some new proofs about Weitjenbock inequality were raised as well.