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

  • and just cut loose like this.

  • 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.

  • Now please release it.

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

  • This flap is below what he's holding.

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

  • because he's in the way, yeah?

  • 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.

  • So, you cannot go from first to second.

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

  • Okay, keep it closed...

  • Now, I'm going to do something

  • And open your eyes

  • What!? It went from the first to the second

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

  • so how did it happen?

  • That's really strange.

  • From this state

  • to this state

  • while this is always being held

  • So, let's do it with eyes open this time

  • Can you hold it again?

  • Now, you can keep the eyes open

  • First I'm going to roll it like this

  • and that's like the pair of handcuffs

  • Or, if you want, you can think of

  • 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

  • loops of the torus

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

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

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A2 初級

可愛的紙上談兵 - Numberphile (Cute Paper Trick - Numberphile)

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    林宜悉 發佈於 2021 年 01 月 14 日
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