On Knotted Necklaces of Pearls
On Knotted Necklaces of Pearls
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珍珠打结项链
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
Ai Oshiro
中科院分区：
文献类型：
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作者：
H. Maehara;Ai Oshiro
一个打结的珍珠项链是一个项链的字符串形成一个不平凡的结。我们假设所有的珍珠都是同样大小的球，并且打结项链中的任何两个连续的珍珠都是相切的。一条打结的项链需要多少珍珠，比如说三叶结？我们证明了15颗珍珠是足够的，而要制作一条可以放在尽可能浅的陈列柜（一个带玻璃盖的盒子）中的打结项链，16颗珍珠是必要和足够的。
A knotted necklace of pearls is a necklace whose string forms a nontrivial knot. We assume that all pearls are balls of the same size, and any two consecutive pearls in a knotted necklace are tangent to each other. How many pearls are necessary to make a knotted necklace, say a trefoil knot? We show that 15 pearls are sufficient, and that to make a knotted necklace which can be put in the shallowest-possible show-case (a box with a glass-lid), 16 pearls are necessary and sufficient.