The mathematics of lacing up

My friend the astrophysicist stumbled upon this article about the relative lengths of shoe lace required by various tying methods.

This really scratched an itch I've had for a while. Whenever I tie my shoes -- I use the American standard zigzag -- the loops turn out so long that they brush the floor. I need to do a second loop to prevent that, but the second loop usually loosens up and then I'm afraid I'll trip.

The article is nice enough to show, through either formulae or a light-ray reflection graphic (I don't know about you, but I read images much better than I read math formulae) that the American uses the least amount of lace. Quite ironic that the oh-so-green Europeans use more lace (although as the graphic shows, not that much more). But the difference between the shoe-shop technique and the other two is quite substantial.

So, I relaced my sneakers to use the shoe-shop technique. And wouldn't you know it? Only one loop required.

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