Garo Nadjarian (Grade 7 – AGBU Boghos K. Garmirian School)

Problem: Can we fold A4 paper equally more than 7 times?

Research:

“If you have a normal sheet of notebook paper and you try to fold it in half multiple times, you probably cannot get it to fold more than 6 times. Maybe 7 if you are really strong. That maximum limit is caused by two things:

1) The number of layers of paper doubles with each fold. So you start with a single layer, then you have two layers, then four, then eight, then 16, then 32, then 64 layers after six folds. Maybe if you are very strong, and you use a pair of pliers, you can get to seven folds and 128 layers, but it probably won’t be pretty.

2) At that point the sheet of paper is so small, and the number of layers so large relative to the small size, and the distortion caused by the folds so great, that there is no way to fold it again. You can’t apply enough leverage, and the fibers of the paper do not have enough flexibility for another fold.

But what if you used a much larger piece of paper, so that you can diminish the effects of fold distortion and paper fiber flexibility? If you use a big enough sheet of paper, you can get to 11 folds, or 2,048 layers, before you reach the limitations of folding. See this video for a demonstration,” said Marshall Brain.

Video: https://www.youtube.com/watch?v=kRAEBbotuIE

Resource: http://www.brainstuffshow.com/blog/why-cant-you-fold-a-piece-of-paper-more-than-seven-times/.

This video shows Mythbusters, a science entertainment program that does experiments based on myths and stories and tell if they are true or not, doing an experiment on this exact problem, with a  football field size paper and manage to fold the paper 11 times by folding it in half proving that you can fold paper more than 7 times but you need a huge paper which is not possible. All other resources tell you that you cannot fold paper more than 7 times because they have used regular notebook or A4 paper and not tried it with a big paper.

Hypothesis:

Hypothesis 1: A4 paper can be folded equally more than 7 times.

Hypothesis 2: A4 paper cannot be folded equally more than 7 times.

Experiment:

Materials: Paper, hands, hammer and an iron.

Procedure: Fold the paper equally as many times as you can with hands. Then use the iron to flatten the folded paper. If needed use the hammer.

Result: Title: The number of folds each student made.

Students	Garo N.	Hagop	Hrag	Arman	Serouj	Georgio	Talar	Anna	Crystel	Garo G.
Number of folds	6	6	7	6	6	6	6	7	6	6

Analysis: Garo N., Hagop, Arman, Serouj, Georgio, Talar, Crystel and Garo G. folded the paper 6 times equally, while Hrag and Anna folded it 7 times equally.

Conclusion: Therefore, an A4 paper cannot be folded more than 7 times. (Hypothesis 2 was verified).