On the angle sum of lines
On the angle sum of lines
复制标题
关于直线的角和
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
T. Zarnócz
中科院分区：
文献类型：
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作者：
F. Fodor;F. Fodor;V. Vígh;T. Zarnócz
欧几里得三维空间中n条线形成的成对（非钝角）角之和的最大值是多少？这个问题是由Fejes Tóth在（Acta Math Acad Sci Hung 10：13-19，1959）中提出的。Fejes Tóth解决了$${n leq 6}$$n≤6的问题，并证明了$${n^{2} pi /5}$n2 π/5的渐近上界为$${n o infty}$$n→∞。他证明了最大值渐近等于$${n^{2} pi /6}$$n2π/6，因为$${n o infty}$$n→∞。本文的主要结果是欧氏空间中n条直线的夹角和的上界渐近等于3 n ^{2} π/16 o infty}$$n→∞。
What is the maximum of the sum of the pairwise (non-obtuse) angles formed by n lines in the Euclidean 3-space? This question was posed by Fejes Tóth in (Acta Math Acad Sci Hung 10:13–19, 1959). Fejes Tóth solved the problem for $${n leq 6}$$n≤6, and proved the asymptotic upper bound $${n^{2} pi /5}$$n2π/5 as $${n o infty}$$n→∞. He conjectured that the maximum is asymptotically equal to $${n^{2} pi /6}$$n2π/6 as $${n o infty}$$n→∞. The main result of this paper is an upper bound on the sum of the angles of n lines in the Euclidean 3-space that is asymptotically equal to $${3n^{2} pi /16}$$3n2π/16 as $${n o infty}$$n→∞.