| 欧氏空间中闭曲线的切线象 |
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| 引用本文： | 丁春华.欧氏空间中闭曲线的切线象[J].西南师范大学学报(自然科学版),1993,18(1):22-25. |
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| 作者姓名： | 丁春华 |
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| 作者单位： | 天津十三中学 |
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| 摘 要： | W.Fenchel曾于1928年证明:3维欧氏空间中光滑闭曲线的切线象的长不小于2π在本文中我们证明了下述定理;定理 设c’是n维欧氏空间中分段光滑闭曲线c的切线象,则必存在一个内接于c’的球面m边形(m≤n+1),其长不小于2π.它是Fenchel定理的推广.
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| 关 键 词： | 闭曲线 切线象 欧氏空间 超平面 |
THE TANGENT SPHERICAL IMAGE OF A COLOSED CURVE IN THE EUCLIDEAN SPACE |
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| Ding Chunhua.THE TANGENT SPHERICAL IMAGE OF A COLOSED CURVE IN THE EUCLIDEAN SPACE[J].Journal of Southwest China Normal University(Natural Science),1993,18(1):22-25. |
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| Authors: | Ding Chunhua |
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| Institution: | Tianjin No. 13 High School |
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| Abstract: | W. Fenchel proved that the lehgth of the tangent spherical image of a closed curve in three-dime-nional Euclidean space is not less than 2n. The following theorem, a generization of Fenchel's, is proved :Let c be a piecewise smooth closed curve in a w-dimensional Euclidean space and d the tangent spherical image of c. Then there is a spherical wi-polygon (m
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| Keywords: | tangent spherical image smooth closed curve Euclidean space |
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