How to turn a sphere inside-out

Amy got me a great book for Christmas — The Math Book (she was inspired by the BoingBoing gushing, here). It goes through the history of math and spends a page on each of 250 different concepts. I’ve been reintroduced to prime numbers and early numerical paradoxes, but I’ve also learned a whole heck of a lot.

Some of it is beyond me, frankly, but author Clifford Pickover does a fantastic job of making each concept accessible to anyone who’s willing to think a little bit. Or, just to dream and let their imagination run a little wild.

There’s been tons already that I think I’d like to blog about, but the one that I read last night and sticks in my head is about turning a sphere inside-out.

Sure, you could poke a hole in a tennis ball, say, and then pull the inside part out through the hole, but that’s against the rules. Mathematically, for a sphere to turn inside out, there can’t be any holes and there can’t be any creases or pinching. Luckily, a sphere can pass through itself. (I tried visualizing a soap bubble, if two bubble films could come together and then come apart on the other side, like water waves, say.

So, can you inside-out a sphere? Turns out you can — but it’s not easy. If you’ve got a few minutes, these videos show you how its done and take you through it.