Can a large circular disk fit into a small square hole? At first you might think that it is an impossible task. However, thanks to Tadashi Tokieda, a mathematician at Stanford University, this task have been proven indeed possible. In fact, it is easier than it sounds. In a Numberphile video, he demonstrates this illusion using cork coasters and paper with a square hole in the middle. By folding the paper in a certain way, the hole suddenly becomes larger and the coaster fits easily into the opening. "I didn't stretch, let alone tear," Tokieda says, "yet if I fold the sheet sensibly, the stud actually goes through a square that's larger than the hole. How is that possible?"
Tokieda then explains in detail how he manages to assemble the stand. "It has to do with the inner or inner dimension of this sheet of paper, which has two dimensions, and the fact that this sheet develops or thrives in the surrounding three-dimensional space," he says. "There's some wiggle room, there's some environmental space."
If you're still scratching your head, be sure to check out How Tokieda Folds Paper. He does this in a special way, transforming a sheet from two dimensions into three dimensions. It connects the two sides of the square and forms a larger opening through which the cup holder easily fits.