| 超球的内接单形的最大体积——献给柯召老师八十诞辰 |
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| 引用本文： | To the —th birthday of our teacher Ko Chao Wu Changjiu and Wang Wanlan.超球的内接单形的最大体积——献给柯召老师八十诞辰[J].成都大学学报(自然科学版),1990(3). |
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| 作者姓名： | To the —th birthday of our teacher Ko Chao Wu Changjiu and Wang Wanlan |
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| 作者单位： | To the 80—th birthday of our teacher Ko Chao Wu Changjiu and Wang Wanlan |
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| 摘 要： | 本文用矩阵分块的技巧和Lagrange乘子法证明在R~n空间内半径为r的超球的内接单形体积V_n〔(n+1)~(n+1)/n~n〕~(1/2)r~n/n!,其中右边是内接正则单形的体积。
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| 关 键 词： | 单形 正则的 超球 不等式 |
The Regular Simplex Incribed In A Hypersphere Has Maximal Volume |
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| Abstract: | The results of 3] imply the following: Of all simplices incrbed in a hypersphere CR~n of radius r, the regularsimplex alone has maximal volume, i. e., V_n≤r~n(n+1)~(n+1)/n~n)~1/~2/n1 (1)where Vn is the volume of any of these simplices. The purpose of this paper is to point out that (1) can be established by amuch more elementary method. |
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| Keywords: | Simplex regular hypersphere inequality |
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