On this episode of our podcast My Favorite Theorem, my cohost Kevin Knudson and I were happy to talk with Katie Steckles, a math communicator from Manchester, England. You can listen to the episode here or at kpknudson.com, where there is also a transcript.

Dr. Steckles’ favorite theorem is a favorite of mine as well: the fold-and-cut theorem. This theorem states that given any shape made with only straight sides, you can fold a piece of paper some number of times and cut the shape out using only one straight-line cut.

As in much of mathematics, the fact that it is theoretically possible to cut any shape out using only one cut does not mean it’s easy. There are two main approaches to finding a fold pattern: the straight-skeleton method and the disk-packing method. A complicated shape is likely to have a complicated, difficult fold pattern. Despite the best efforts of the letter S, Dr. Steckles has learned to fold and cut every letter of the alphabet, as she displays virtuosically in this video for Numberphile.

Her fold patterns became the basis for this font designed by Erik and Martin Demaine.

In each episode of the podcast, we ask our guest to pair their theorem with food, beverage, art, music or other delight in life. Dr. Steckles decided on a nice warm bowl of her husband’s chili to pair with the fold-and-cut theorem. You’ll have to listen to the episode to find out why it makes such a good accompaniment to folded paper.

As befits a math communicator, Dr. Steckles exists in many places online; her website, Twitter, and the Aperiodical blog are good places to start. She is also involved in organizing MathsJam, or MathJam, a monthly math pub night that takes place in many cities around the world. If you’re interested in finding or organizing a Math(s)Jam near you, check out their website.

You can find more information about the mathematicians and theorems featured in this podcast, along with other delightful mathematical treats, at kpknudson.com and here at Roots of Unity. A transcript is available here. You can subscribe to and review the podcast on iTunes and other podcast delivery systems. We love to hear from our listeners, so please drop us a line at myfavoritetheorem@gmail.com. Kevin Knudson’s handle on Twitter is @niveknosdunk, and mine is @evelynjlamb. The show itself also has a Twitter feed: @myfavethm and a Facebook page. Join us next time to learn another fascinating piece of mathematics.

Previously on My Favorite Theorem: