Name: Cute Paper Trick - Numberphile
Uploaded: 2020-03-30T05:57:24.000Z
Duration: 2 min 9 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Well, this object is made from a single sheet of paper

Modal verbs - A2

And Brady, can you hold this flap, please?

Ok, we shall call this the "first state",

so, this flap is, um, above what he's holding.

He can hold it like this and this is going to be the "second state", ok?

Now, you cannot go from the first state to the second state

And you cannot, you know, go from the first to the second.

Well, if these are made of rubber, something flexible,

then I can stretch it and pass it over his body and come back underneath

But it's not rubber, I mean, it's real paper, so you can't do this.

Now, please close your eyes for a moment, and...

What!? It went from the first to the second

And he was holding this all the time and he didn't let it go

circle here and then imagine another imaginary circle which makes it a torus

And I, mathematician like to say I "reverse" the orientation of both generators of the torus

And they do this, and then that keeps the orientation and I'm on the other side.