Fold Paper 42 Times to Reach the Moon? (Exponential Growth)

Step by step

1. Fold paper in half 42 times · how thick?
   Fold a sheet of paper in half, forty-two times. How thick is it?
2. A book? A building? The Moon?
   As thick as a book? A building? Or all the way to the Moon?
3. Each fold doubles: 0.1 mm × 2^n
   Each fold doubles the thickness. Paper is about a tenth of a millimeter. So after n folds, it's zero point one millimeters, times two to the n.
4. 10 folds ≈ 10 cm · 20 folds ≈ 105 m
   Ten folds: about ten centimeters, a thick book. Twenty folds: over a hundred meters, a skyscraper.
5. 30 folds ≈ 107 km · 42 folds ≈ 440,000 km
   Thirty folds: over a hundred kilometers, past the edge of space. Forty-two folds: about four hundred forty thousand kilometers. Past the Moon!
6. Doubling: slow, then explosive · exponential growth
   Doubling starts slow, then explodes. That's exponential growth.
7. 2002: Britney Gallivan folded paper 12 times
   But can you really fold it? People used to say paper can't be folded more than eight times. In two thousand two, high schooler Britney Gallivan folded a twelve hundred meter strip of toilet paper twelve times.
8. Grab a sheet · how many folds can you get?
   Grab a sheet and try. How many folds can you get?
9. On a test: 0.1 × 2^42 mm ≈ 440,000 km
   On a test: the thickness is zero point one times two to the n millimeters. With forty-two folds, that's about four point four times ten to the eleventh millimeters. That's about four hundred forty thousand kilometers, past the Moon.