| 非欧几何中极限三角形面积有限性的简单证明 |
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| 引用本文： | 张影,朱鹏. 非欧几何中极限三角形面积有限性的简单证明[J]. 扬州大学学报(自然科学版), 2007, 10(3): 22-24 |
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| 作者姓名： | 张影 朱鹏 |
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| 作者单位： | 扬州大学,数学科学学院,江苏,扬州,225002 |
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| 摘 要： | 给出双曲非欧几何中极限三角形面积有限性的另外一种简单证明.方法是将只有一个顶点在无穷远处的极限直角三角形分划成一序列四边形,使得每一个四边形的面积小于前一个四边形面积的一半.
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| 关 键 词： | 非欧几何 极限三角形 面积有限性 |
| 文章编号： | 1007-824X（2007）03-0022-03 |
| 修稿时间： | 2007-05-11 |
A simple proof of finiteness of areas of asymptotic triangles in non-Euclidean geometry |
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| ZHANG Ying,ZHU Peng. A simple proof of finiteness of areas of asymptotic triangles in non-Euclidean geometry[J]. Journal of Yangzhou University(Natural Science Edition), 2007, 10(3): 22-24 |
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| Authors: | ZHANG Ying ZHU Peng |
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| Affiliation: | CoU of Math Sci, Yangzhou Univ, Yangzhou 225002, China |
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| Abstract: | Another simple synthetic proof of finiteness of areas of asymptotic triangles in non-Euclidean geometry is given.To this end,a right-angled asymptotic triangle with exactly one vertex at the infinity is dissected into a sequence of quadrilaterals so that the area of each such quadrilateral is less than half the previous one. |
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| Keywords: | non-Euclidean geometry asymptotic triangles finiteness of areas |
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