Intermath | Workshop Support

 Write-up

Paper Folding
Problem Statement
If a piece of paper could be folded in half fifty times, what would be the thickness of the folded paper? A ream (500 sheets) of paper is 2 inches thick.

(Source: Mathematics Teaching in the Middle School, Nov-Dec 1995).

Submit your idea for an investigation to InterMath

Problem setup

Here, I am being asked to figure out how thick a sheet of paper will be if it is folded 50 times.

Plans to Solve/Investigate the Problem

After pondering this question for a short time, I immediately thought to put this in an Excel spreadsheet.

Investigation/Exploration of the Problem

I must admit that I am feeling particularly lazy today, so I picked a problem that is easy for me.

Picture this:  I have a sheet of paper that is … let’s just call it P units thick.  If I fold it, I will essentially have one sheet of paper that is 2 sheets thick or 2P units thick.

When I make another fold, I am really folding 2P units over.  This means that the thickness will be doubled yet again!  This gives me a thickness of 2*2P = 4P.

Doing my folding once more, I am doubling 4P: 2*4P= 8P.

At this point, I have no desire to keep this up 47 times more!  (I already told you I was feeling a bit lazy, so you simply must cut me some slack!)  I will move to the wonders of Microsoft to finish this.

The table below contains a formula to calculate the progressive thicknesses using an exponential equation.

 Thickness # of Folds 0.004 Flat sheet 0.016 1 fold 0.032 2 fold 0.064 3 fold 0.128 4 fold 0.256 5 fold 0.512 6 fold 1.024 7 fold 2.048 8 fold 4.096 9 fold 8.192 10 fold 16.384 11 fold 32.768 12 fold 65.536 13 fold 131.072 14 fold 262.144 15 fold 524.288 16 fold 1048.576 17 fold 2097.152 18 fold 4194.304 19 fold 8388.608 20 fold 16777.216 21 fold 33554.432 22 fold 67108.864 23 fold 134217.728 24 fold 268435.456 25 fold 536870.912 26 fold 1073741.824 27 fold 2147483.648 28 fold 4294967.296 29 fold 8589934.592 30 fold 17179869.18 31 fold 34359738.37 32 fold 68719476.74 33 fold 137438953.5 34 fold 274877906.9 35 fold 549755813.9 36 fold 1099511628 37 fold 2199023256 38 fold 4398046511 39 fold 8796093022 40 fold 17592186044 41 fold 35184372089 42 fold 70368744178 43 fold 1.40737E+11 44 fold 2.81475E+11 45 fold 5.6295E+11 46 fold 1.1259E+12 47 fold 2.2518E+12 48 fold 4.5036E+12 49 fold 9.0072E+12 50 fold

WOW!  This paper can get pretty thick!  Keep in mind that the measurement is in inches, and the E+blah blah blah,  means the preceding digits times 10 to the blah blah power!

Author & Contact.
Michelle Houston.  Feel free to contact me