Transcript:

So, how many times can you fold a paper in half? And your knee-jerk answer might be 6, 7, or 8, or whatever number you come up with. But you can derive it. So, if you think about it, if you fold a paper in half, the thickness doubles. And then, if you have a long sheet of paper, you can just fold it in one direction. And you can derive a formula for it. This is it. This is the formula for one-directional paper folding. Or you can choose to fold it lengthwise first, then widthwise next, then lengthwise again. So, in alternate direction folding, you can derive another formula—this one. And the constraint is: you cannot fold anymore when the width is less than the thickness of the stack of paper. Except, these formulas that I derived are approximately correct—but precisely wrong. This one is the correct formula. It's derived by Britney Gallivan, who holds the world record for folding paper. She folded paper 13 times. And her formula—go back and see it—her formula has pi. Now, tell me where pi comes in her formula. She added some feature that I missed. You tell me what feature.