平面上任意凸多边形面积的计算

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英文篇名：The Calculation of the Area of Arbitrary Convex Polygon on the Plane 作者：廖祥超 ; 郭民之 英文作者：LIAO Xiang-chao;GUO Min-zhi;School of Mathematics,Yunnan Normal University; 关键词：平面凸多边形 ; 顶点逆时针排序 ; 面积公式 ; Excel程序化计算 英文关键词：convex polygon on the plane;;vertex with anticlockwise sort;;formula of area;;programming calculation in excel 中文刊名：DNZS 英文刊名：Computer Knowledge and Technology 机构：云南师范大学数学学院; 出版日期：2016-11-30 16:58 出版单位：电脑知识与技术 年：2016 期：v.12 语种：中文; 页：DNZS201628103 页数：3 CN：28 ISSN：34-1205/TP 分类号：251-252+255

摘要

以平面上任意有限个点为顶点的凸多边形面积的计算是一个很有实用价值的问题,该文结合平面解析几何相关知识,用数学归纳法先推导出平面上凸n边形面积的一般计算公式,然后利用Excel中多个函数和排序技巧实现了面积的程序化计算,并用实例演示说明。最后讨论了如何用这种方法去计算平面上任意凸多边形的面积。
        It is a quite practical and valuable problem about the calculation of the area of convex polygon which is formed by arbitrary point on the plane. Based on the relative knowledge of Analytic Geometry, the formula for the calculation of the area of convex polygon was deduced and proved by Mathematical Induction in this paper; then many functions and skills of sorting were used in Excel, which helps it realize the goal of programming calculation of the area of convex polygon in the example. Finally, they discussed this method about the calculation of the area of arbitrary convex polygon on the plane.

引文

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