**Britney Crystal Gallivan** (born 1985) of

Pomona, California, is best known for determining the maximum number of times which paper or other thickness 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 maximum number of times any piece of paper could be folded in half was seven. Gallivan succeeded in folding a very long sheet of toilet paper in half 12 times. She calculated that instead of folding in half every other direction, the least volume of paper to get 12 folds would be to fold in the same direction, using a very long sheet of paper. A special kind of $85-per-roll toilet paper met her length requirement. Not only did she provide the empirical proof, but she also derived an equation that yielded the width of paper or length of paper necessary to fold a piece of paper of thickness

*t* any

*n* number of times.

She was a keynote speaker at the September 22, 2006 National Council of Teachers of Mathematics convention.

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

- <math>

W = pi t 2^.</math>

For single-direction folding (using a long strip of...

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