Everytime you fold a paper it doubles in thickness.
Start with .1mm
Folds thickness
1 .2
2 .4
3 . 8
4 1.6
5 3.2
So you can see in 5 folds our paper has grown to 32x the thickness. Imagine 37 more folds.
In fact given that we start with 0.1mm our thickness follows a nice relation that is t = (2^x ) /10 where x is the number of folds.
For example X = 2, t = 0.4mm
So using 42 we get t = (2^42 ) / 10 mm = 439804651110.4 mm or
439804 km
The distance between the earth and moon is
384,400
So you can see on the 41st fold we would be at a thickness of ~200,000 km and with one more fold we would be past the moon.
A piece of paper is notionally 0.004 inches thick. The moon is 238,000 miles away. That’s nearly four quadrillion sheets of paper stacked up to reach the moon. Surely just 42 folds isn’t that thick? But wait. Every time you fold a piece of paper, you double its thickness. So multiply two times two times two and so on forty-two times, or by exponent notation 2^42 . Turns out that really is a huge number, more than enough thicknesses to make it to the moon.
Another popular demonstration of the power of doubling: start with a penny. Double it every day. In a month you will be a millionaire. If you kept doubling it for 42 days you would own the whole world, I think, though I haven’t done the math. I leave it as an exercise for the student.
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