Britney Gallivan's Record-Breaking Paper Folding Feat

Hello, I'm Brittany Gallivan

Have you ever heard the commonly accepted belief that no one can fold a piece of paper

or anything in half more than eight times

That was six folds for this piece of paper. Back in 2001, my honors pre-calculus instructor challenged anyone in the class to fold anything

in half 12 times. This is a sheet of gold foil, four inches by four inches, 11 millionths of an inch thin

It is actually thinner than the wavelength of visible light. I folded the four by four inch gold foil in half 12 times

My teacher stated that he had misspoken and that the challenge was actually to fold any

piece of paper in half 12 times. The paper folding challenge is often used as an example of exponential growth

If you fold paper in half 50 times, you could reach the sun

Every time you fold the paper, these double. What people weren't taking into account for was the radius section

In an initial fold, the radius section is minimal. As the folds get larger, this radius section takes up more and more paper

Although this doubles, the amount of paper that you need in the radius section for each

fold actually squares. As your number of folds increases, you need four times the length to achieve the next fold

Where's my pen? Oh. I derived two limiting equations for folding anything in half

One was for single direction folding. I'm solving for length pi times the thickness over six multiplied by two to the n plus four

times two to the n minus one. And then the second equation was for alternate directional folding

Width is going to equal pi times thickness times two to the three n minus one divided

by two. I researched online and found paper that was 33,007 inch thin that was 4,000 feet in length

I quickly realized that material this thin was not going to work because the slightest

breeze would ruin the attempt. I found a space called The Village at Indian Hill in Pomona

It had a long corridor that would suffice to take on this challenge

After eight hours of crawling on the mall floor, I was able to successfully fold the

paper in half 12 times. This here is the 11th fold. It's great to be in the record books and to finally set the paper folding record straight

I hope that others can look at this challenge and take it on themselves and maybe even expand

on it and take on their own impossible challenges