A common claim states that a sheet of paper cannot be folded in half more than seven times. But is this true? How many times can you fold a piece of paper?
In 2002, Britney Gallivan, then a middle schooler in Pomona, California, folded a single piece of paper in half 12 times. She is currently holding Guinness World Record (opens in a new tab) for most times to fold a sheet in half.
“Before I attempted, it was the accepted belief that it was impossible to fold a piece of paper in half more than eight times, and seven folds was the commonly accepted folding limit,” Gallivan told LiveScience in an email. “I was the first person ever to fold paper half nine, 10, 11 and 12 times.”
Gallivan didn’t just set a world record; she also came up with equations to calculate how many times a piece of paper can be folded in half in one or more directions. She described these equations in her book “How to fold paper half a dozen times (opens in a new tab)(Historical Society of Pomona Valley, 2002).
The call that led Gallivan to achieve these feats was an additional credit challenge i had to class to throw everything in half 12 times, according to the Historical Society of Pomona Valley (opens in a new tab). She folded a thin sheet of paper gold foil 12 times. The teacher then changed the challenge to folding something thicker: a piece of paper.
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“I started working on the problem by spending many hours trying to fold sheets of paper, newspapers and any other flat material I could find,” Gallivan said. “This is the first approach most people take to try to solve the problem. It was very frustrating, as I had many failed attempts at trying to fold different papers in half. I started asking about all those who had tried the problem before me was right that it might be impossible to fold paper in half more than eight times.”
However, “I could not accept that folding in half could be limited,” Gallivan recalled. “I knew I either needed to meet the challenge or understand what was limiting the folding progression.”
The equations that Gallivan came up with calculated how many times a sheet of paper could be folded. She found that to fold a piece of paper in half many times, a long thin sheet is needed – the more a sheet is folded, the thicker the resulting stack becomes, and when the stack is thicker than it is long, there is nothing left to fold . She eventually set her record with a sheet of tissue paper she found online that was 4,000 feet (1,219 meters) — more than three-quarters of a mile, or over a kilometer — long, Guinness World Records noted. Setting the record took about eight hours of crawling down a long corridor in a mall in California, she recalled.
“Working on the problem took a tremendous amount of time and effort,” Gallivan said. “As frustrating as it was at times, it was a fun and exciting endeavor. I learned an enormous amount from the experience, which has been valuable to me throughout my life in more capacities than one might expect.”
Since Gallivan set her record, others have made claims of folding a sheet of paper more than 12 times.
“I applaud the efforts of others who try to take on the challenge, as I know full well how difficult it can be,” Gallivan noted. “However, some of the methods used have included stacking separate pieces on top of each other, taping pieces together, cutting paper, tearing paper and pleating fan folds instead of folding in half. These attempts to break the record have not met the requirements of the challenge, as they bypass the principles of the mathematical geometric progression of paper folding and demonstrate a misunderstanding of why the challenge was thought to be impossible.”
Still, “I expect my current record to be surpassed,” Gallivan said. “I wish everyone the best of luck with paper folding, but I want to make sure that the foundation of the challenge, and what makes this problem so wonderful, is not lost in the process.”
Anyone trying to beat Gallivan’s record should expect an incredibly thick pile of paper. For example, after 42 folds, a sheet about 0.1 millimeter thick would be more than 273,280 miles (439,800 kilometers) high — greater than the average distance between the Earth and the Moon, according to Boundless brilliance (opens in a new tab)a Los Angeles-based STEM education non-profit organization.
All in all, Gallivan hopes that others “shoot for the moon or even the sun, which they will reach by the fiftieth fold!”