| 双曲类二次曲线外切多边形中有向面积的定值定理及其应用 |
| |
| 引用本文： | 喻德生.双曲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].福州大学学报(自然科学版),2004,32(5):522-525. |
| |
| 作者姓名： | 喻德生 |
| |
| 作者单位： | 南昌航空工业学院信息与计算科学系,江西,南昌,330034 |
| |
| 基金项目： | 南昌航空工业学院科研基金资助项目(EC200407040) |
| |
| 摘 要： | 利用有向面积定值法,对双曲线外切多边形中对角线三角形和切点线三角形之间的关系进行研究.得到双曲类二次曲线外切n边形(n≥4)中有向面积的一个定值定理,并据此推出双曲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.
|
| 关 键 词： | 双曲线外切多边形 有向面积 定值 共点 共线 |
| 文章编号： | 1000-2243(2004)05-0522-04 |
| 修稿时间： | 2003年11月25 |
On a fixed value theorem for directed areas in hyperbolic circumscribed polygons and its applications |
| |
| YU De-sheng.On a fixed value theorem for directed areas in hyperbolic circumscribed polygons and its applications[J].Journal of Fuzhou University(Natural Science Edition),2004,32(5):522-525. |
| |
| Authors: | YU De-sheng |
| |
| Institution: | YU De-sheng(Department of Information and Computation Sciences, Nanchang Institute of Aeronautical Technology, Nanchang, Jiangxi 330034, China) |
| |
| Abstract: | Using the fixed value method of directed areas, we research the relationship between two kinds of triangles in hyperbolic circumscribed polygons thoroughly. We obtain a fixed value theorem for directed areas in hyperbolic circumscribed polygons, and thus deduce as many as n(n-3) concurrent points of three lines in hyperbolic circumscribed polygons, and the famous Brianchon Theorems for elliptic circumscribed hexagons and quadrilaterals, etc. |
| |
| Keywords: | hyperbolic circumscribed polygon directed area fixed value concurrent collinear |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《福州大学学报(自然科学版)》浏览原始摘要信息 |
| 点击此处可从《福州大学学报(自然科学版)》下载免费的PDF全文 |
