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


                                  

 

 

writeup.htm Failed! Click Here To Go Back!