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  • So say you just moved from England to the US

  • and you've got your old school supplies from England

  • and your new school supplies from the US

  • and it's your first day of school and you get to class

  • and find that your new American paper doesn't fit in your

  • old English binder.

  • The paper is too wide, and hangs out.

  • So you cut off the extra and end up with all these strips of paper.

  • And to keep yourself amused during your math class

  • you start playing with them.

  • And by you, I mean

  • Arthur H. Stone in 1939.

  • Anyway, there's lots of cool things

  • you can do with a strip of paper. You can fold it into shapes.

  • And more shapes.

  • Maybe spiral it around snugly like this.

  • Maybe make it into a square.

  • Maybe wrap it into a hexagon with

  • a nice symmetric sort of cycle to the flappy parts.

  • In fact, there's enough space here to keep wrapping the strip,

  • and then your hexagon is pretty stable.

  • And you're like, "I don't know, hexagons aren't too exciting,

  • but I guess it has symmetry or something."

  • Maybe you could kinda fold it

  • so the flappy parts are down and the unflappy parts are up.

  • That's symmetric, and it collapses down into these three triangles,

  • which collapse down into one triangle, and collapsible hexagons are,

  • you suppose, cool enough to at least amuse you a little bit during your class.

  • And then, since hexagons have six-way symmetry,

  • you decide to try this three-way fold the other way,

  • with flappy parts up, and are collapsing it down

  • when suddenly the inside of your hexagon decides to open right up.

  • What? You close it back up and undo it.

  • Everything seems the same as before,

  • the center is not open-uppable.

  • But when you fold it that way again,

  • it, like, flips inside-out. Weird.

  • This time, instead of going backwards,

  • you try doing it again. And again. And again. And again.

  • And you want to make one that's a little less messy,

  • so you try again with another strip and tape it nicely

  • into a twisty-foldy loop. You decide

  • that it would be cool to color the sides,

  • so you get out a highlighter and make one yellow.

  • Now you can flip from yellow side to white side.

  • Yellow side, white side, yellow side, white side

  • Hmm. White side? What? Where did the yellow side go?

  • So you go back, and this time you color the white side green,

  • and find that your paper has three sides.

  • Yellow, white, and green.

  • Now this thing is definitely cool.

  • Therefore, you need to name it.

  • And since it's shaped like a hexagon and you flex it

  • and flex rhymes with hex, hexaflexagon it is.

  • That night, you can't sleep because you keep thinking

  • about hexaflexagons.

  • And the next day, as soon as you get to your math class

  • you pull out your paper strips.

  • You had made this sort of spirally folded paper

  • that folds into again, the shape of a piece of paper,

  • and you decide to take that

  • And use it like a strip of paper to make a hexaflexagon.

  • Which would totally work, but it feels sturdier

  • with the extra paper.

  • And you color the three sides and are like,

  • Orange, yellow, pink.

  • And you're sort of trying to pay attention to class.

  • Math, yeah. Orange, yellow, pink.

  • Orange, yellow, white? Wait a second.

  • Okay, so you color that one green.

  • And now it's orange, yellow, green. Orange, yellow, green.

  • Who knows where the pink side went?

  • Oh, there it is. Now it's back to orange, yellow, pink.

  • Orange, yellow, pink. Hmm. Blue.

  • Yellow, pink, blue. Yellow, pink, blue. Yellow, pink, huh.

  • With the old flexagon, you could only flex it one way,

  • flappy way up.

  • But now there's more flaps. So maybe you can fold it both ways.

  • Yes, one goes from pink to blue,

  • but the other, from pink to orange.

  • And now, one way goes from orange to yellow,

  • but the other way goes from orange to...neon yellow.

  • During lunch you want to show this off

  • to one of your new friends, Bryant Tuckerman.

  • You start with the original, simple, three-faced hexaflexagon,

  • which you call the trihexaflexagon.

  • And he's like, whoa!

  • and wants to learn how to make one.

  • And you're like, it's easy! Just start with a paper strip,

  • fold it into equilateral triangles,

  • and you'll need nine of them, and you fold them around

  • into this cycle and make sure it's all symmetric.

  • The flat parts are diamonds, and if they're not,

  • then you're doing it wrong.

  • And then you just tape the first triangle to the last

  • along the edge, and you're good.

  • But Tuckerman doesn't have tape.

  • After all, it was invented only 10 years ago.

  • So he cuts out ten triangles instead of nine,

  • and then glues the first to the last.

  • Then you show him how to flex it by pinching around a

  • flappy part and pushing in on the opposite side to make it

  • flat and trianglly, and then opening from the center.

  • You decide to start a flexagon commitee together

  • to explore the mysteries of flexagation.

  • But that will have to wait until next time.

So say you just moved from England to the US

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B1 中級

六面體 (Hexaflexagons)

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    林宜悉 發佈於 2021 年 01 月 14 日
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