September 30, 2015

Make Your Own Font, 1 Cut at a Time

Move over, four-color theorem! It's time for the one-cut theorem: You can cut out any shape you want with one cut if you're willing to do some clever folding

By Evelyn Lamb

Single-cut initials. Like Katie Steckles, I find the "negatives" delightful.

Join Our Community of Science Lovers!

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American

In an excellent Numberphile video, Katie Steckles (previously appearing on this blog here and here) tells us about the fold and cut theorem: any region with straight sides can be created by folding a piece of paper and cutting it out with a single straight cut. I'll let her explain.

To me, the fold and cut theorem is a perfect illustration of the peculiar laziness of mathematicians. We’ll work for hours to find a way around a twenty-minute computation, and in this case, we’ll fold paper for hours to avoid opening and closing the scissors a few extra times.

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

A single-cut square within a square, or the letter O in my fold-and-cut alphabet.

Towards the end of the video, in a virtuoso fold-and-cut demonstration, Steckles folds 26 pieces of paper from memory and produces the whole alphabet in 26 cuts. I spent some time this afternoon in my office folding a few letters of my own. There are some resources out there for fold-and-cut guidance, but I followed Steckles’s advice and tried to figure them out myself. I had some early successes, some pretty weird failures, and a lot more fun than if I had looked up the answers. Although my initial goal was to cut out the letters of my and my office mate’s names to put on our door, I ended up settling on just my initials for now.

Making one-cut letters is a math activity anyone old enough to use scissors can enjoy. Mike Lawler and his two kids have been folding and cutting shapes during the past week, so if you’re a parent or teacher who wants to try it with kids you might get some ideas from them. I think I'll be incorporating one-cut letters into sewing projects for math friends, and I can only hope someone will create a font based on a fold-and-cut alphabet.

Take that, four color theorem! One cut suffices.

It’s Time to Stand Up for Science

If you enjoyed this article, I’d like to ask for your support. Scientific American has served as an advocate for science and industry for 180 years, and right now may be the most critical moment in that two-century history.

I’ve been a Scientific American subscriber since I was 12 years old, and it helped shape the way I look at the world. SciAm always educates and delights me, and inspires a sense of awe for our vast, beautiful universe. I hope it does that for you, too.

If you subscribe to Scientific American, you help ensure that our coverage is centered on meaningful research and discovery; that we have the resources to report on the decisions that threaten labs across the U.S.; and that we support both budding and working scientists at a time when the value of science itself too often goes unrecognized.

In return, you get essential news, captivating podcasts, brilliant infographics, can't-miss newsletters, must-watch videos, challenging games, and the science world's best writing and reporting. You can even gift someone a subscription.

There has never been a more important time for us to stand up and show why science matters. I hope you’ll support us in that mission.

Thank you,

David M. Ewalt, Editor in Chief, Scientific American