| 内接于平面凸闭曲线的多边形面积和周长取得极值的必要条件 |
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| 引用本文： | 李世运,刘秀兰.内接于平面凸闭曲线的多边形面积和周长取得极值的必要条件[J].东北林业大学学报,1992(1). |
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| 作者姓名： | 李世运 刘秀兰 |
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| 作者单位： | 东北林业大学
(李世运)，东北林业大学(刘秀兰) |
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| 摘 要： | 平面上任一光滑的凸闭曲线的内接多边形,其面积取得极值的必要条件是:曲线在每一顶点处的法线与该点相邻两顶点的连线垂直;其周长取得极值的必要条件是:曲线在每一顶点处的法线平分该顶角。
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| 关 键 词： | 面积 周长 极值 |
NECESSARY CONDITION TO OBTAIN THE EXTREMUM OF THE AREA AND THE GIRTH OF THE POLYGON INSCRIBED WITH CONVEX, CLOSED AND SMOOTH CURVE ON A PLANE |
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| Li Shiyun Lu Xiulan.NECESSARY CONDITION TO OBTAIN THE EXTREMUM OF THE AREA AND THE GIRTH OF THE POLYGON INSCRIBED WITH CONVEX, CLOSED AND SMOOTH CURVE ON A PLANE[J].Journal of Northeast Forestry University,1992(1). |
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| Authors: | Li Shiyun Lu Xiulan |
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| Institution: | Northeast Forestry University |
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| Abstract: | The necessary condition, under which the area of the polygon inscribed on a convex, closed and smooth curve on a plane attains the extremum, is that the normal line at the every apex on the curve is perpendicular to the line which connects the two nearest points on the two sides of the apex. The necessary condition, under which the girth attains the extremum, is that the normal line at the apex on the curve equally divides the vertex angle. |
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| Keywords: | Area Girth Extremum |
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