Algebra Teachers: Use this trick when introducing geometric sequences.
Take a sheet of notebook paper.Tear it in half.
Place the two pieces together and tear in half again.
Ask how many pieces of paper you have. (Hopefully, they will answer 4).
Now ask the class this question,
"If I were able to keep tearing the paper in half and put the sheets together,
and I did this thirty times, how high would the stack of paper be?"
Tell the class that the average sheet of paper is .001 inches thick.
Do not let your students use calculators!
Just have them give you a guess at first.
Now have them construct a table and look for a pattern:
| # of tears | Pieces of Paper | Height of Pile |
|---|---|---|
| 1 | 2 pieces of paper | .002" thick |
| 2 | 4 pieces of paper | .004" thick |
| 3 | 8 pieces of paper | .008" thick |
| 4 | 16 pieces of paper | .016" thick |
| 5 | 32 pieces of paper | .032" thick |
| 6 | 64 pieces of paper | .064" thick |
| 7 | 128 pieces of paper | .128" thick |
| 8 | 256 pieces of paper | .256" thick |
| ... | ... | ... |
| 30 | 230 = 1,073,741,824 pieces of paper | 89,478 feet thick |
So, the pile of paper would be 16.94 miles high!!!!
Of course, you can't tear the stack of paper more than about 7 times.
A related problem is the Paper Folding Problem.
The challenge is to fold a piece of paper in half more than seven or eight times,
using paper of any size or shape. The task was commonly thought to be impossible.
However, in January of 2002, Britney Gallivan folded a piece of paper in half
twelve times! In April of 2005 Britney's accomplishment was mentioned on the prime
time CBS television show Numb3rs.
Click here for the Pomona Historical Society's article about Britney.
