The Secret of Floppy Paper
In this video, mathematician Tadashi Tokieda shows us a simple demo with surprising implications. He takes two squares of ordinary paper, clips them together, and shows how they either stick together or flop apart, depending on how they're held (basically upside down and right side up). The weird thing is that the pieces of paper change their behavior based on where you hold them. If you hold them on one edge, they flop. On the next edge, they stick. Next edge, flop again. Why?
Most forms of paper are anisotropic, meaning the material behaves differently when oriented in different directions. A shorthand term might be to say the paper has a grain. This makes sense, because wood has a grain—a direction in which the fibers run—so the paper does too, unless it's been intentionally broken up.
Knowing that materials can be anisotropic, what does that tell us? How does this apply to making paper books? And how can we use this knowledge to amaze children? Watch this video and learn. (Bonus points: You'll also learn about corrugation in this video, and why corrugated cardboard is so strong.)
More Numberphile videos featuring Tokieda: Can You See These Freaky Dot Patterns? and The Spinning Tube Trick.