Name: 忘れられたフレクサゴン - Numberphile (The Forgotten Flexagon - Numberphile)
Uploaded: 2021-01-14T10:17:02.000Z
Duration: 12 min 31 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

But it's always the hex of flex again that you see one based on the hex against got six edges and so I have some good bye Hearts has made a whole series of videos about these things.

I'm going to go for the forgotten flex again The Tetra flex again one with four edges And to make it, we're gonna use a square of paper.

It's the first step is to fold it in half whichever way you want them both the same.

And one of the reasons why I love the Tetra Flex again is you don't need any gluten.

If you're making any of the hex of flex against, you have to get some glue and stick bits together, whereas this one is just folding and cutting.

So the first half and half has split it into four sections.

And if I make the creases really like good creases because they're going to kind of be used as hinges later, I should end up with.

It's a piece of paper now split into 16 smaller squares.

I'm going to remove the center four squares.

I'm gonna keep this ring of 12 squares intact.

You could do that by stabbing the citizen, just cutting around.

But as we learned from case tickles in her fault and cut their own video, you can do anything you want in a single cot.

If you're a bit clever about how you fold it.

So this is now gonna be three easy steps and one difficult step.

So we start on the left and we go around clockwise.

Take the four on the outside for them up and over.

Take three of the top fold them up in Nova and they come down like that Next step as we keep coming around, take these three for the muffin over and that is the end of the easy steps.

The only difficult step is when you take up the bottom ones.

You want to lift these up as if we did it before that first fault?

So where you've got to do is move the original fold out of the way without ruining it.

Then lift this one up and make sure the bit next to it goes underneath.

So we kind of take all of this bit next to it and just feed through into its underneath and the rest should follow and just kind of snap into place.

And they are there is your four edged flex again, The Tetra flex again.

So what's amazing about the tent reflects again is it's got a lot of faces.

So we got face one on the front here, which I'm gonna number with ones.

And then if we fold it over, I guess ones on the front, we got twos on the backs of face one and face too.

And then on the other side of the ones we've got, what's blank.

This is a shit with at least three faces.

And what happens is every time you fold it closed one way so unfolding with one's closed with the twos on the outside, I can open up on the opposite side so it closes this way.

But then I open it the other way around and I get a new face.

Label this one four, but and then let's see if we fold this this way.

We're looking for six faces because if we think of the original shape we made was marrying a 12 12 on the front.

There's 12 on the back, so I've got 24 of these little squares.

So there are enough squares can make six whether or not it does have a slightly different question.

Thank you for that label is when he has six.

And if we actually wanna check that, we've got all of them face to in face one folded in face.

Okay, We could pull the whole thing apart.

So if we pumped back out again, disassemble it.

Okay, So there's or the fate was number every single square at some point to make all of them.

There are two different ways to put this back together.

And if you do it the wrong way, you will get the mirror image.

But if I carefully put it back together the same way we folded originally we're back where we started.

And when you make one of these kind of fun, you play with it for a while.

If you've not made one before, it takes a bit to work out where all the faces are.

Obviously, you don't have to just put numbers.

If you were one of these doodling mathematicians, you would draw pictures or, you know, the artistic.

I've just numbered it, which is a bit sad.

So I've numbered it, so you could be as creative as you want, and you could spend a while trying to find them.

But if you are in the numbers after, why you, like, hang on, I know they're only six faces, but what combinations of faces can I get the same time?

Obviously, I can get one opposite, too, because when I started with, I can get three opposite one.

Can I get five opposites like what combinations of faces can you see at the same time?

And that was the first thing I started wondering where I take one of these, and for awhile I thought I knew you could get combinations of faces, but there's always one of the two.

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忘れられたフレクサゴン - Numberphile (The Forgotten Flexagon - Numberphile)

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