圆内接(外切)多边形面积的极值性质  

Extremal properties on inscribed (circumscribed) polygons of a circle

作　　者：彭祥华 李经文[2] 

机构地区：[1]邵东六中,湖南邵东422809 [2]邵阳学院,湖南邵阳422000

出　　处：《湖南科技学院学报》2005年第5期46-47,共2页Journal of Hunan University of Science and Engineering

摘　　要：关于定圆的内接n边形,本文用两种方法证明了,圆的内接正n边形面积最大.关于圆的外切多边形,本文引入了对偶多边形这一新的概念,从而得到了如下结果,在定圆的所有外切n边形中,以外切正n边形面积最小.In this paper by two methods we prore that the area of inscribed regular n- polygons of a circle is maximal than areas of all inscribed n-polygons of that circle. On circumscribed polygons of a circle, we introduce a new concept—dual polygon. And so is obtained the following result: area of circumscribed regular n-polygons of a circle is minimal in all circumscribed n-polygons of that circle.

关 键 词：外接多边形 内切多边形 极值 对偶多边形 迭代法 圆 面积 

分 类 号：O174.1[理学—数学]