How many times can you fold a piece of paper in half?
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 junior in high school in Pomona, California, folded a single piece of paper in half 12 times. She currently holds the Guinness World Record for the most times to fold a sheet of paper in half.
"Prior to my endeavor, it was the accepted belief that folding a piece of paper in half more than eight times was impossible and seven folds was the commonly accepted folding limit," Gallivan told Live Science in an email. "I was the first person to ever fold paper in 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 any piece of paper can be folded in half in a single direction or multiple directions. She detailed these equations in her book "How to Fold Paper in Half Twelve Times" (Historical Society of Pomona Valley, 2002).
The prompt that led Gallivan to accomplish these feats was an extra-credit challenge in math class to fold anything in half 12 times, according to the Historical Society of Pomona Valley. She folded a sheet of thin gold foil 12 times. The teacher then changed the challenge to folding something thicker: a piece of paper.
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"I began working on the problem by spending many hours trying to fold paper sheets, newspapers, and any other flat material I could find," Gallivan said. "This is the first approach most people use to attempt to solve the problem. It was very frustrating, as I had many unsuccessful attempts at trying to fold different papers in half. I began to question if all those who had attempted the problem before me were correct that folding paper in half more than eight times could very well be impossible."
However, "I could not accept that folding in half could be limited," Gallivan recalled. "I knew I needed to either accomplish 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 in order 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 once the stack becomes thicker than it is long, there is nothing left to fold. She ultimately 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 crawling in a long corridor in a shopping 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 exhilarating endeavor. I learned an immense amount from the experience, which has been valuable to me throughout my life in more capacities than one would 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 attempting to take on the challenge, as I know very well how difficult attempting it can be," Gallivan noted. "However, some of the methods used have included stacking separate pieces on top of one another, taping pieces together, cutting paper, tearing paper, and pleated fan folding instead of folding in half. These efforts to break the record have not adhered to the requirements of the challenge, as they circumvent 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 anticipate that my current record will be surpassed," Gallivan said. "I wish everyone the best success with their paper-folding endeavors but want to make sure the foundation of the challenge, and what makes this problem so marvelous, is not lost in the process."
Anyone who does seek to break Gallivan's record should expect an incredibly thick stack of paper. For example, after 42 folds, a sheet about 0.003 inch (0.1 millimeter) thick would be more than 273,280 miles (439,800 kilometers) high — greater than the average distance between Earth and the moon, according to Boundless Brilliance, a Los Angeles-based STEM education nonprofit.
All in all, Gallivan hopes others "shoot for the moon or even the sun, which they will reach after the fiftieth fold!"
