凸多边形面积表达式的注记  

A Note on the Expression of Convex Polygon Area

作　　者：李卫高[1] 宋晓奎[2] LI Wei-Gao;SONG Xiao-kui(Luohe Medical College,Luohe Henan 462002,China;Xingtai University,Xingtai Hebei 054001,China)

机构地区：[1]漯河医学高等专科学校,河南漯河462002 [2]邢台学院,河北邢台054001

出　　处：《大学数学》2018年第6期67-69,共3页College Mathematics

摘　　要：以凸四边形为例,通过建立其面积表达式,利用拉格朗日乘数法,给出了其周长为定值时面积最大情况;推广此方法,得到了任意定周长凸多边形为正多边形时面积最大的结论.Taking a convex quadrangle as an example,whose maximum area with fixed perimeter is obtained by establishing the area function,using the Lagrange method of multipliers.Applying this method,the maximum area of a convex polygon with fixed perimeter reached when it is a positive polygon,is proved.

关 键 词：凸多边形 最大面积 拉格朗日乘数法 

分 类 号：O13[理学—数学]