利用凸函数的性质证明几何命题

Application of Convex Function to Prove Geometric Propositions

讨论了凸函数的性质,然后利用凸函数的这些性质和Jensen不等式,证明有关三角形中内角和边的几个不等式,显示出凸函数在证明几何命题中的作用.

In this paper , by using Jessen inequality we prove some inequalities ahout angles and sides of a triangle,and prove that area of inscribed regular n-polygons of a circle is maxmal in all inscribed, and area of cumscribed regular n-polygons of a circle is minmal in all cumscribed.