Britney Gallivan

Britney Gallivan (born c. 1986) of Pomona, California is best known for determining the maximum number of times which paper or other non-compressible materials can be folded.

Biography

In January 2002, while a junior in high school, Gallivan demonstrated that a single piece of toilet paper, 4000 ft (1200 m) in length, can be folded in half twelve times. This was contrary to the popular conception that the number of times any piece of paper could only be folded in half was limited to eight times. She also folded a single square sheet of gold foil in half twelve times. Not only did she provide the empirical proof, but she also derived an equation that yielded the width of paper, "W", needed in order to fold a piece of paper of thickness "t" any "n" number of times.

Gallivan's story was mentioned in the episode "Identity Crisis" [ [http://pomonahistorical.org/12times.htm Folding Paper in Half 12 Times] ] of "Numb3rs" on CBS in 2005 and on an episode of "MythBusters" [ [http://kwc.org/mythbusters/2007/04/episode_72_underwater_car_and.html Annotated Mythbusters] ] on The Discovery Channel in 2007.

In 2007 Gallivan graduated from UC Berkeley with a degree in Environmental Science from the College of Natural Resources.

Paper folding theorem

An upper bound and a close approximation of the actual paper width needed for alternate-direction folding is

:$W\; =\; pi\; t\; 2^\{(3/2)left(n-1\; ight)\}.$

For single-direction folding (using a long strip of paper), the exact required strip length "L" is

:$L\; =\; frac\{pi\; t\}\{6\}left(2^\{n\}+4\; ight)left(2^\{n\}-1\; ight).$ Where t represents the thickness of the material to be folded and n represents the number of folds desired.

These equations indicate two things: that in order to fold anything in half, it must be $pi$ times longer than its thickness; and that depending on how something is folded, the amount its length decreases with each fold differs.

See also

* Mathematics of paper folding

References

External links

* [http://pomonahistorical.org/12times.htm Historical Society of Pomona Valley Page]
* [http://mathworld.wolfram.com/Folding.html Folding at MathWorld]
* [http://www.its.caltech.edu/~ari/paper-folding.html Independent verification of equation at Caltech]
* [http://www.research.att.com/~njas/sequences/A076024 Entry for the folding function] at the "On-Line Encyclopedia of Integer Sequences"