Mental Floss

Mathematician Shows How to Make Any Shape From a Single Cut

Caitlin Schneider

Mathematicians don’t approach the world quite like the rest of us. Case in point: Katie Steckles. The Manchester-based mathematician was trying to cut a square out of a piece of paper and started to wonder about the most efficient way to do so. Her queries led her to some experimentation (turns out it can be done with one snip), and then to the pub, where she wondered aloud whether there were other shapes that could be made with one cut. Her companion asked, “Isn’t that a theorem?”

Indeed it is. The fold-and-cut theorem, which first appeared in 1721—and was later proved by MIT computer scientist/computational origami wizard/former child prodigy Erik Demaine—asserts that any shape comprised of straight lines can be made from a single cut if you can just figure out the right way to fold the paper. Stars, turtles, the entire alphabet—which Steckles demonstrates in the Numberphile video above—can all be crafted. The concept is pretty mind-blowing and, as you’ll learn from Steckles, might’ve even earned Betsy Ross her place in history. 

[h/t The Kids Should See This]