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  • Unbeknownst to many, there are two ways of tying your shoelace. You see, the first step is usually like this.

  • In the second step, you can

  • either

  • do it like this,

  • in which case,

  • you see, the knot becomes kind of perpendicular to the direction of the lace at the end.

  • Or, you can do exactly the mirror image of what you have just done.

  • And it is slightly wrong, actually, when you do this.

  • But that's a nice way to do it.

  • When you do that,

  • in this case, the knot becomes kind of parallel, if you see what I mean, to the shoelace.

  • What did I do? So, there are two ways of doing it, right? You can do, start from, like, this,

  • or the other direction. So let's do it in this direction, in some sense.

  • Now, that determines one of the orientations.

  • So, one way to do it is to, from my point of view, the right hand, and pull it over, and then do this,

  • which produces a

  • perpendicular knot.

  • The other way is

  • to make the loop with my

  • left hand, and then turn it over and through, and then make the knot, in which case

  • the knot becomes parallel to the shoelace. That's quite interesting. Now, it turns out that these two things have a difference.

  • And I'd like to show one of the differences. Which is also a nice trick to know in practice, in daily life. Let's make a knot

  • by first doing this, and then, secondly,

  • by doing that. If you think of this as a mirror, this is not

  • symmetric with respect to this mirror. Because you see, this strand goes under this loop, whereas this one goes over this loop.

  • It's kind of more like a, you know,

  • rotation symmetry. Whereas if I put them in this configuration, that's symmetric, in the sense that they're both going under.

  • And you can see that it is symmetric. Now,

  • Brady: "So which one matches which shoelace?"

  • I think this one matches the parallel one, and the rotation one matches the perpendicular one.

  • I'm not entirely sure about this. You explore. Okay.

  • So, let's make a tight knot with this. And this is a fairly tight knot. This was the symmetric one.

  • And, you know, if you wanted to undo this knot, you have to go in, and it's really a bothersome.

  • But there is actually a nice trick to undo this knot.

  • Let me show it to you first. I hold it like this. It comes straight off.

  • What did I do?

  • Let's do it in slow motion and in detail. Again, this is the symmetric one. And when I

  • close it, it's like that.

  • You grab those two or those two. It doesn't matter which one, let's. And when you pull them taut,

  • you get the straight line.

  • And it turns out that the knot, the entire knot, can slide across the, along the straight line.

  • And it just comes off the end

  • and undoes itself.

  • So this kind of symmetric knot is quite fragile.

  • Or, if you like, if you knotted it like this, as far as it's somewhere in the middle,

  • it's quite tight, and it's, it's secure. But if you want to untie it,

  • you don't have to go in and mess around with just undoing that, I need to, a little bit.

  • You can pull it off, slide it off completely. Whereas, if you made the other

  • rotational knot, which one is it? It's I think this one.

  • Brady: "This is a the asymmetric."

  • Asymmetric one. And this one goes over, this one goes under. It's not symmetric with respect to the similar.

  • That's a very secure knot. You can't really undo it. The only way to undo it is to actually go in.

  • So it's useful to know, by the way.

  • You know, what is this thing? It certainly has a lot of crossings. But again

  • we're looking for the minimal number of crossings, so we try to untangle this and open it up as much as we possibly can.

  • And if you're patient enough and do that

Unbeknownst to many, there are two ways of tying your shoelace. You see, the first step is usually like this.

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レースの結び目のトリック - Numberphile (Lace Knot Trick - Numberphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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