25 References 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/theshoelace-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. 所以我們應該怎樣穿鞋帶呢？這視乎你想選 擇使用更少鞋帶的綁法，還是採取更穩妥的方法。 如果要在最短的長度和最大的穩妥程度之間取個 平衡，交叉綁法似乎是個最佳選擇，所以在沒有 數值在手的情況下你應該選擇這種綁法；雖然領 結綁法也能給你可接受的穩妥程度，它至少不會 使你的鞋子分開兩截。然而這些數值其實也近在 手邊，只要你有尺子、網絡（或《科言》實體書） 和追根究底的「八卦」天性就足夠；最後一樣尤 其重要，有了它，你就幾乎能解決任何迎面而來 的問題。 You can measure h as a ratio on shoes with n pairs of eyelets, and compare n with the corresponding value of hn in the table. As I write this I’m wearing a pair of shoes laced by the crisscross method: They have 4 pairs of eyelets and h with value roughly 0.4, so obviously I made the right decision when I laced them. Of course, most shoes in stores today are made with h very close to hn, so whichever lacing you use will be quite strong regardless [6]. So how should you lace your shoes? It depends on whether you prioritize shorter or stronger lacings. The one that best balances minimal length and maximal strength seems to be the crisscross, so without other information you should go for that one, although bowtie can give a reasonable strength that at least your shoes won’t fall apart. But such information is always at your fingertips if you have a ruler, internet access (or a copy of Science Focus), and an inquiring mind. The last one is the most important of these – with that in hand, you can find answers to almost any question that comes your way.

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