Here’s something you’ve probably never thought much about: Is there a way to get a round disk through a smaller square hole in a piece of paper?
It seems silly, right? Of course not, you say! It’s impossible!
Well, not always, according to this video by Numberphile featuring a mathematician from Stanford University, Tadashi Tokieda. If you fold it up just the right way, the round object will go through easily.
According to Tokieda, “It has to do with the intrinsic, or inner dimensions of the sheet of paper, which is two dimensions, and the fact that the sheet evolves and flourishes in the three dimensional space.”
Still confused? We don’t blame you.
Basically, by messing with the paper (but not breaking it), you can create a straight line out of two of the four sides of the square.
Move it in the right way, and boom – you’ve got yourself a big hole to put the disk through. But the cool bit is that moving it the right way means moving the 2D paper into the 3D plane by folding it up off the table.
“When we do this manoeuvre, you are allowing the whole thing to come out into 3D, and then come back down,” Tokieda explains in the video.
“The fact you can escape into the ambient third dimension and come back in… gives you this wonderful magic.”
The pictures really help if you’re not getting it, so we recommend checking out the video below to see the experiment in action.
If you need us, we’ll be at the bar, betting our friends that we can fit a large round coaster through a smaller square hole in a sheet of paper.