# Paper Folding Fun

On this Sunday morning, I am yet again the owner of a losing lottery ticket.  I know.  I know.  The probability of winning is so slim, why waste my money?  I figure that \$1 a week isn’t too much to spend on a little bit of hope, and some of the proceeds fund the Bright Futures Scholarships that help some of my own students.

But, I don’t want to get into a lottery discussion here.  No, I’d rather talk a little bit about the paper on which the disappointing numbers were printed.  I have this absentminded habit of folding paper in my hands, especially if it is destined for the trash.  I did this with the lottery ticket, while my son was sitting nearby.  And I felt the need to launch into an exploration on how many times I could fold my ticket before I couldn’t go further.

I started out with 0 folds, a paper that was 1 layer in thickness.  I folded it once, in half.  This resulted in 2 layers of thickness.  I folded it again, now having 4 layers of thickness.  And again, resulting in 8 layers of thickness.  Do you see a pattern so far?  The number of folds and the number of layers are related by powers of 2.  Raise 2 to the number of folds, and you have the number of paper layers.

As I commented on this, my son groaned something along the lines of “Do you have to turn this into a math discussion?”  To which I replied, “Why, yes, yes, I do.”  And I kept folding.

I managed to get it to 6 folds or 2^6 = 64 layers.  After that, the paper was too thick to force another fold.  And then I got curious about how far people have gone in this quest.  So, I relied on trusty Google and found an article with a couple of good embedded videos.

Turns out, the myth is that the paper can only be folded 7 times.  The first video on the site below is a Mythbusters episode that sought out to test this myth.  I’m not going to share their results.  Just watch the video.  If you like big things and heavy power equipment, then you may enjoy their experiment.

As I read further, I learned about a young lady named Britney Gallivan who actually derived a paper folding theorem and then used toilet paper to prove it could be folded 12 times.  Her findings are fascinating.  Near the bottom of the page, there’s a video of a group using toilet paper at MIT to take this experiment to another level.  So fun!  I encourage you to read and view at the link below.  And, if you are inclined to do your own paper folding, please don’t hesitate to share your results in the comments.  Happy Sunday Funday!

How Many Times Can You Fold a Piece of Paper?