| 抛物类二次曲线外切多边形中有向面积的定值定理及其应用 |
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| 引用本文： | 喻德生.抛物类二次曲线外切多边形中有向面积的定值定理及其应用[J].大学数学,2006,22(1):26-29. |
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| 作者姓名： | 喻德生 |
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| 作者单位： | 南昌航空工业学院,信息与计算科学系,南昌,330034 |
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| 基金项目： | 南昌航空工业学院校科研和教改项目 |
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| 摘 要： | 利用有向面积定值法,对抛物线外切多边形中的对角线三角形和切点三角形之间的关系进行研究,得到抛物类二次曲线外切n边形(n≥4)中有向面积的一个定值定理,并据此推出抛物线外切多边形中三线共点的点多达n(n-3)个,以及射影几何中著名的Brianchon定理等结论.
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| 关 键 词： | 抛物线外切多边形 (有向)面积 定值 共点 共线 |
| 文章编号： | 1672-0454（2006）01-0026-04 |
| 收稿时间： | 2004-12-02 |
| 修稿时间： | 2004年12月2日 |
On a Fixed Value Theorem for Directed Areas in Parabolic Circumscribed Polygons and its Applications |
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| YU De-sheng.On a Fixed Value Theorem for Directed Areas in Parabolic Circumscribed Polygons and its Applications[J].College Mathematics,2006,22(1):26-29. |
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| Authors: | YU De-sheng |
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| Abstract: | Using fixed value method of directed areas,we research the relationship between two kinds of triangles in parabolic circumscribed polygons thoroughly.We obtain a fixed value theorem for directed areas in parabolic circumscribed polygons,and thus deduce as many as n(n-3) concurrent points of three lines in parabolic circumscribed polygons and the famous Brianchon Theorem for parabolic circumscribed hexagons and quadrilaterals,etc.,easily. |
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| Keywords: | parabolic circumscribed polygon (directed)area fixed value concurrent collinear |
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