「緊密」綁法還有多一個額外條件，就是鞋帶必須在A、B行之間交錯，不能包含垂直線段。圖二顯示三種最常見的緊密綁法，分別是交叉綁法（crisscross）、歐洲綁法（European）和鞋店綁法（shoe-store）[2]：

• 當h < hn，交叉綁法最為穩妥；
• 當h = hn，兩種綁法同樣穩妥；
• 當h > hn，鞋店綁法最為穩妥。

 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

#### 參考資料：

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