The Math of Folding paper Monika Craciuenscu

How many times can you fold a piece of paper in half? Take a piece of paper and try it for yourself. How many times can you fold your piece of paper in half? We’re going to have a Q&A time to see if you can find the answer. – FYI: This may end up being very very short.

Directions: Think of some questions you can ask to answer the question. You must think of questions that can be answered by a “yes” or “no” response. If the response to your question is yes, you may ask another question. You may not ask if a number is the answer to the question presented to you. Use your reasoning to come up with a number you might be right and keep it to yourself. HINT: It was believed that anyone could fold a piece of paper only 7 times until someone broke the record.

What was your conclusion? The answer, as of now, is 12 times.

May I present… A lady named Britney Gallivan has held a record for folding a piece of paper 12 times. This is a well known challenge of folding paper in half more than seven or eight times, using a single piece of paper of any size or shape. She derived Gallivan folding equations which tells anyone how many times a single piece of paper can be folded in half. She’s written a book on it and has derived folding techniques that excede 12 folds, including a 16- fold technique. Imagine that!!!

Here’s an example Gallivan Equation The exact equation for the single direction folding case. L is the minimum possible length of the material, t is material thickness, and n is the number of folds possible in one direction.

But why? A good answer would be exponential growth. – What is exponential growth? – Growth rate of the value of a mathematical function which is proportional to the function's current value. So the greater number of folds, the smaller the area of the shape (whatever you’re using to fold) and the harder it is to fold. – Unless, you use a creative technique!!!

n2**nkm (0.1*10**-6 * 2**n)Comment x 10** x 10** x 10** x 10**-6finger nail thickness x 10** x 10** x 10** x 10**-6thickness of a notebook x 10** x 10** x 10**-3width of a hand (incl. thumb) x 10** x 10**-30.4m height of a stool x 10** x 10**-31.6m: an average person's height (yeah, a short guy) x 10** x 10** x 10**-313m height of a two story house x 10** x 10** x 10**-3quarter of the Sears tower (440m) At thirty folds you have reached the sun from the earth. At sixty folds you have the diameter of the solar system. At 100 folds you have the radius of the universe.