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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.

• 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