「紧密」绑法还有多一个额外条件，就是鞋带必须在A、B行之间交错，不能包含垂直线段。图二显示三种最常见的紧密绑法，分别是交叉绑法（crisscross）、欧洲绑法（European）和鞋店绑法（shoe-store）[2]：

• 当h < hn，交叉绑法最为稳妥；
• 当h = hn，两种绑法同样稳妥；
• 当h > hn，鞋店绑法最为稳妥。

 n 3 4 5 6 7 8 9 10 hn 0.9029 0.7412 0.645 0.5794 0.5309 0.4931 0.4625 0.4372

#### 参考资料：

1. Polster, B. (2002). What is the best way to lace your shoes? Nature, 420, 476. https://doi.org/10.1038/420476a
2. Stewart, I. (1996). Arithmetic and old lace. Scientific American, 275(1), 94-97. https://www.jstor.org/stable/24993276
3. Stewart, I. (2006). How to Cut a Cake and Other Mathematical Conundrums. Oxford University Press.
4. Peterson, I. (2020, October 30). The Shoelace Problem. The Mathematical Tourist. http://mathtourist.blogspot.com/2020/10/the-shoelace-problem.html.
5. Halton, J. H. (1992). The shoelace problem (No. 92-032). Department of Computer Science, UNC Chapel Hill.
6. Polster, B. (2006). The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace Your Shoes. American Mathematical Society.

2024年6月