Can computers discover ideal knots?
Can computers discover ideal knots?
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DOI：
10.1080/10586458.2003.10504499
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发表时间：
2003-01-01
影响因子：
0.5
通讯作者：
Rawdon, EJ
中科院分区：
文献类型：
--
作者：
Rawdon, EJ
我们讨论多边形结能量和光滑结能量之间的关系，重点关注绳索长度。我们证明，平滑结可以以绳长值接近的方式刻在多边形结中。对于给定的结类型，我们证明存在多边形绳长度最小值，并且最小多边形绳长度收敛到光滑结类型的最小绳长度。这些多边形的子序列收敛到平滑的绳索长度最小值。因此，对多边形结执行的绳长最小化实际上近似于平滑结的绳长最小化。
We discuss the relationship between polygonal knot energies and smooth knot energies, concentrating on ropelength. We show that a smooth knot can be inscribed in a polygonal knot in such a way that the ropelength values are close. For a given knot type, we show that polygonal ropelength minima exist and that the minimal polygonal ropelengths converge to the minimal ropelength of the smooth knot type. A subsequence of these polygons converges to a smooth ropelength minimum. Thus, ropelength minimizations performed on polygonal knots do, in fact, approximate ropelength minimizations for smooth knots.