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A paper folded 42 times would reach the moon

At first the title of this post might seem ridiculous but its true. If it was possible to fold a sheet of paper 42 times it would be thick enough to reach the moon. Here is the explanation
 
Each time you fold a paper it doubles in thickness. Zero folds=1 sheets tick, one fold=2 sheets thick, two folds=4 sheets thick. This follows the rule where the thickness (in sheets) is equal to two raised to the number of folds or
t(sheets)=2#folds
To convert from number of sheets thick to a dimension we just multiply by the thickness of one sheet (varies by type but .1mm is a good average). Where .1mm is 10-4 meters. So thickness in meters is given by the equation
T(m)=(10-4)*2#folds
 
So if we want the thickness to be the distance to the moon (3.939*108 meters) we plug that into the equation and solve for # of folds
3.939*108=(10-4)*2#folds
3.939*1012=2#folds                              :solving for an exponent requires that we take the natural log of both sides so we can pull the exponent down
ln(3.939*1012)=ln(2#folds)
ln(3.939*1012)=#folds*ln(2)
# folds=ln (3.939*1012)/ln(2)
# folds=41.8                                  :You can't take .8 folds of something so we have to round up to 42 folds
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So if we fold a paper 42 times it's thickness is going to be given by the following equation
T=10-4*242 meters
T=4.39 *108 meters
 
So it actually extends past the moon by 45,000km or 28,000 miles.
As a note its very hard to fold paper more than 7 times, or anything more than 13 times. I don't think anythings been folded more than 15 times, certainly not 20 and 42 times is easily impossible.

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Jared G.

Math and Physics from Elementary to University

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