凸多边形闭区域的参数方程及应用  

The Parametric Equation of Closed Convex Polygonal Region and Application

作　　者：李盛 阮建苗[2] 

机构地区：[1]浙江省衢州第一中学,浙江衢州324000 [2]浙江外国语学院理工学院,浙江杭州310012

出　　处：《浙江外国语学院学报》2011年第3期79-85,共7页Journal of Zhejiang International Studies University

基　　金：浙江省教育厅科研项目(Y201018469)

摘　　要：得到了平面凸多边形闭区域的一种较为简洁的参数方程.作为应用,给出了与凸多边形闭区域相关的求面积与最值等问题.特别地,给出了Jensen不等式的几何解释,并由此推广了一些已知的结果.最后,进一步讨论了几个与凸多边形闭区域相关的未解决的问题.Obtained in this paper is a simpler parametric equation of closed region in planar encircled by convex polygon.As an application,given in the paper is calculating area and maximum and minimum and other issues associated with the closed region encircled by convex polygon.Especially,it gives a geometric interpretation of the Jensen inequality,and thus generalizes some known results.At last,some open problems associated with the closed region encircled by convex polygon are also discussed.

关 键 词：凸多边形 平面闭区域 参数方程 JENSEN不等式 

分 类 号：O182[理学—数学]