| 欧氏平面上建立对偶的一种方法 |
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| 引用本文： | 梁亦孔. 欧氏平面上建立对偶的一种方法[J]. 上海工程技术大学学报, 2006, 20(3): 240-244. DOI: 10.3969/j.issn.1009-444X.2006.03.012 |
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| 作者姓名： | 梁亦孔 |
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| 作者单位： | 上海工程技术大学,基础教学学院,上海,201620 |
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| 基金项目： | 上海市重点学科建设项目 |
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| 摘 要： | 在欧氏直角坐标系下通过点与直线的非齐次坐标来研究点与直线之间特殊的对偶原则.解决了射影几何中点与直线度量关系无法建立对偶的问题.在欧氏几何中建立起了角平分线,两条直线垂直、线段长度、点到直线的距离的对偶命题.
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| 关 键 词： | 对偶 欧氏几何 点和线度量关系 |
| 文章编号： | 1009-444X（2006）03-0240-05 |
| 收稿时间： | 2006-04-20 |
| 修稿时间： | 2006-04-20 |
Method of Establishing Duality Principle for Euclidean Plane |
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| LIANG Yi-kong. Method of Establishing Duality Principle for Euclidean Plane[J]. Journal of Shanghai University of Engineering Science, 2006, 20(3): 240-244. DOI: 10.3969/j.issn.1009-444X.2006.03.012 |
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| Authors: | LIANG Yi-kong |
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| Affiliation: | College of Fundarmental Studies, Shanghai University of Engineering of Science, Shanghai 201620, China |
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| Abstract: | Through the study of nonhomogeneous coordinates of points and lines,the special duality principle between points and lines was handled in Euclidean system of rectangular coordinates and the question of how to construct duality between points and lines in projective geometry was answered.At the same time,the duality propositions of the angular bisector,two perpendicular lines,the length of the line segment,the distance between a point and a line in Euclidean geometry,were also established. |
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| Keywords: | duality Euclidean geometry metric relations of points and lines |
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