Buzz
Folding a sheet of paper might seem easy, but in reality, it becomes extremely challenging as we witness the power of exponential calculations.
Is it true that a sheet of paper can't be folded more than seven times? How many times can you fold a piece of paper?
In 2002, Britney Gallivan, a middle school student in Pomona, California, folded a sheet of paper 12 times, securing the Guinness World Record.
'Before my attempt, it was believed that folding a piece of paper more than eight times was impossible, and seven times was the accepted folding limit. I was the first to fold the paper 9, 10, 11, and 12 times,' Gallivan told Live Science.
Interestingly, Gallivan's motivation for these feats came from a math class challenge where she had to fold anything as many times as possible. In the first attempt, Gallivan folded a thin, gold-colored paper about 12 times. The teacher then changed the challenge to folding something thicker, which happened to be a sheet of paper.
Not only breaking the world record, but Gallivan also devised equations to calculate how many times any piece of paper could be folded, be it in one direction or multiple. Specifically, her equations computed the folds a sheet of paper could endure. She realized that for multiple folds, the paper itself must be both thin and long. The more it's folded, the thicker it becomes. When the thickness surpasses the length, there's nothing left to fold. This compelled Gallivan to search for a suitable material.
'I spent hours folding various papers, newspapers, and any flat material I could find', Gallivan said.
Finally, Gallivan set her record with a silk paper she found online, measuring a staggering 1.219 meters, documented in the Guinness World Records. To achieve this, Gallivan crawled for about 8 hours through a long corridor in a shopping center in California to unfold the paper.
Since Gallivan set her record, others claimed to fold a paper more than 12 times. In fact, anyone attempting to surpass Gallivan's record must contend with an unexpectedly thick stack of paper. This is purely mathematical logic.
Folding a sheet of paper is far from easy, mathematically speaking
For instance, an average sheet of paper is about 0.1 mm thick. With each fold, the thickness of the entire paper stack you hold doubles. Fold 1, thickness is 0.2 mm; fold 2, it's 0.4 mm - and you still think this is manageable. By the 8th fold, the thickness is 0.1 x 2^8 = 25.6 mm, equivalent to the width of a 250-page book. On the 12th fold, it's as tall as a chair. On the 17th fold, the thickness matches a 2-story building. Continue the calculations, and you'll witness the power of exponential math - specifically, the powers of 2.
For example, after 42 folds, the paper would be as thick as 439,800 km - surpassing the average distance between Earth and the Moon. By the 51st fold, your paper would exceed the Sun's thickness, around 200 million km. Ultimately, with 103 folds, your paper would surpass 100 billion light-years, larger than the observable universe's diameter (~93 billion light-years).
Another challenge is the difficulty in folding paper. The thicker the paper, the greater the pressure needed to fold it. As you attempt multiple folds, the inner layers along the fold line get compressed, while the outer layers need more tension due to the larger folding angle. This uneven tension resists your folding, making folding a paper already folded eight times much more challenging than folding a 250-page book.
While human hands struggle to fold paper too many times, even specialized devices like hydraulic presses 'give up' on folding paper. In a video on the Hydraulic Press Channel on Youtube, an A3-sized paper was continuously folded six times, then had to resort to a hydraulic press. On the seventh fold, the paper exploded, turning into a shattered piece resembling hard plastic. By the eighth fold, the pressure was sufficient to break even the folded crease. The folded crease collapsed as if you were snapping a piece of plastic, creating an incredibly loud noise.
So, folding paper may seem easy, but in reality, it becomes unbelievably challenging!
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