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To me this is not very surprising to me, since in Germany there exists a well-known children's game called "Durch eine Postkarte steigen" ("step through a postc

To me this is not very surprising to me, since in Germany there exists a well-known children's game called "Durch eine Postkarte steigen" ("step through a postcard"), where - as the naming suggests - you have to step through a postcard while you are only allowed to use scissors to cut the postcard in a clever way. Here a German YouTube video that shows how it is done (you don't have to understand anything that is spoken, since I think the video is quite self-explanatory): > https://www.youtube.com/watch?v=ynoLSTsrRhs https://www.youtube.com/watch?v=ynoLSTsrRhs

Dangeranger 9y ago
Children in the USA play that game as well, but the moment when he shows that the gap in the 2D space is expanded to the two sides of the square by folding into 3D space is still amazing. I screamed out loud it was so much fun to see.
dandare 9y ago
I think that is a different principle.
- wolfgke 9y ago
  > I think that is a different principle. I don't think so. In both cases we have some object with the property that the "perimeter of the convex hull of a 2D projection of it" is too large to fit the object through some hole in the paper. On the other hand, the length of the border of the hole in the paper is at least as large as this perimeter. So we twist the paper around such that the object passes through.
cortesoft 9y ago
Mr. Wizard had an episode where he did this same thing: https://www.youtube.com/watch?v=LjAboqBeGpE https://www.youtube.com/watch?v=LjAboqBeGpE
jonshariat 9y ago
I think the reason the example in the video is so interesting is that its non-destructive. It only involves bending and the paper and coaster remain intact.
- wolfgke 9y ago
  > I think the reason the example in the video is so interesting is that its non-destructive. It only involves bending and the paper and coaster remain intact. There is a quadratic hole cut into the quadratic paper (which I would clearly call "destructive"). It is just not shown in the video how the quadratic hole is cut into the quadratic paper. If this argument does not convince you, here is another one: Also for stepping through a postcard after the hole is cut it is just bending the paper.
  - Too 9y ago
    Ehh. They way you initially cut the paper constraints how you later can fold it. If the square was cut any smaller you wouldn't be able to fit the coaster through no matter how you try to fold the paper. The square and its size is a constant in this problem, using a scissor to make the square bigger after its given to you would be considered destructive. In the postcard problem there is no such constraint as you are allowed to cut in whichever form/size you want.

Dangeranger 9y ago

Children in the USA play that game as well, but the moment when he shows that the gap in the 2D space is expanded to the two sides of the square by folding into 3D space is still amazing. I screamed out loud it was so much fun to see.

dandare 9y ago

I think that is a different principle.

wolfgke 9y ago
> I think that is a different principle. I don't think so. In both cases we have some object with the property that the "perimeter of the convex hull of a 2D projection of it" is too large to fit the object through some hole in the paper. On the other hand, the length of the border of the hole in the paper is at least as large as this perimeter. So we twist the paper around such that the object passes through.

cortesoft 9y ago

Mr. Wizard had an episode where he did this same thing: https://www.youtube.com/watch?v=LjAboqBeGpE https://www.youtube.com/watch?v=LjAboqBeGpE

jonshariat 9y ago

I think the reason the example in the video is so interesting is that its non-destructive. It only involves bending and the paper and coaster remain intact.

wolfgke 9y ago
> I think the reason the example in the video is so interesting is that its non-destructive. It only involves bending and the paper and coaster remain intact. There is a quadratic hole cut into the quadratic paper (which I would clearly call "destructive"). It is just not shown in the video how the quadratic hole is cut into the quadratic paper. If this argument does not convince you, here is another one: Also for stepping through a postcard after the hole is cut it is just bending the paper.
- Too 9y ago
  Ehh. They way you initially cut the paper constraints how you later can fold it. If the square was cut any smaller you wouldn't be able to fit the coaster through no matter how you try to fold the paper. The square and its size is a constant in this problem, using a scissor to make the square bigger after its given to you would be considered destructive. In the postcard problem there is no such constraint as you are allowed to cut in whichever form/size you want.