Can a large circular disk fit through a small square hole? When you first picture it, it seems impossible. But thanks to Stanford University mathematician Tadashi Tokieda, you'll see that it is possible and easier than you might think. In an enlightening video by Numberphile, he demonstrates this illusion by using a cork coaster and a sheet of paper with a square hole cut into the middle of it. By folding the paper a certain way, the hole suddenly becomes large enough for the coaster to easily pass through the opening.
“I didn’t stretch, let alone tear,” Tokieda shares, “and yet when I fold the sheet back in a judicious way, the coaster does go through the square that is bigger than the hole. How is this possible?”
Tokieda then goes into a detailed explanation of how he’s able to make the coaster fit. “It has to do with the intrinsic, or inner dimension, of this piece of paper, which is two dimensions, and the fact that this sheet evolves, or flourishes, in the ambient three-dimensional space,” he says. “There is some elbow room, there is some ambient space.”
If that still leaves you scratching your head, be sure to watch how Tokieda folds the paper. He does so in a specific manner that transforms the sheet from two to three dimensions. In doing that, he brings two sides of a square together and forms a larger opening for which the coaster can pass through without a problem.
Scroll down to see Tokieda in action. Then, try it for yourself!
It seems like a large circular disk cannot fit into a smaller square hole, right? Watch how mathematician Tadashi Tokieda proves the math illusion possible:
h/t: [IFL Science!]