What Can Tiling Patterns Teach Us?
The Joy of Why
Steven Strogatz, Janna Levin and Quanta Magazine
4.9 • 577 Ratings
🗓️ 3 July 2024
⏱️ 40 minutes
🧾️ Download transcript
Summary
In the tiling of wallpaper and bathroom floors, collective repeated patterns often emerge. Mathematicians have long tried to find a tiling shape that never repeats in this way. In 2023, they lauded an unexpected amateur victor. That discovery of the elusive aperiodic monotile propelled the field into new dimensions.
The study of tessellation is much more than a fun thought exercise: Peculiar, rare tiling formations can sometimes seem to tell us something about the natural world, from the structure of minerals to the organization of the cosmos. In this episode, co-host Janna Levin speaks with mathematician Natalie Priebe Frank on the subject of these complex geometric combinations, and where they may pop up unexpectedly. Specifically, they explore her research into quasicrystals — crystals that, like aperiodic tiles, enigmatically resist structural uniformity.
Transcript
Click on a timestamp to play from that location
| 0:00.0 | For thousands of years, cultures around the world have explored patterns with tiles, from ancient mosaics to stone floors to modern subway tiles. |
| 0:10.0 | Perhaps for just as long, mathematicians have been enthralled by the way different shapes can or can't fit together to cover a plane, like a tabletop or a wall, |
| 0:20.0 | and by the complex geometric combinations they've uncovered. |
| 0:23.6 | For decades, the search was on for a single tile |
| 0:27.6 | that might fill a plane in an a periodic pattern, |
| 0:30.6 | which is to say one that has no repeats. |
| 0:33.6 | Then in March, |
| 0:34.6 | 2023, David Smith, an amateur tiling enthusiast, found a single tile that resisted repetition, at least as far as his attempts could take him. |
| 0:45.1 | Could this be the elusive, a periodic monotile? |
| 0:52.4 | I'm Janelle Levin, and this is The Joy of Why, a podcast from Quantum Magazine, |
| 0:58.0 | where I take turns at the mic with my co-host, Steve Strogetz, exploring the biggest questions in math and science today. |
| 1:06.0 | In today's episode, we'll speak with Natalie Preeby-Frank to ask why the discovery of the |
| 1:20.1 | aperiodic monotile is so significant and what tessellations, which are tight arrangements of shapes |
| 1:27.1 | over surfaces, what tessellations, which are tight arrangements of shapes over surfaces, |
| 1:28.5 | what tessalations might reveal about the natural world? |
| 1:32.0 | Natalie is a professor of mathematics and statistics at Vassar College. |
| 1:36.7 | Her research is primarily on mathematical models for physical solids, |
| 1:41.9 | and her research is also on quasi-crystals, which are ordered materials |
| 1:46.2 | that resemble crystals but lack a consistently repeating structure. Natalie, we're so glad to have |
| 1:53.2 | you with us and that you're bringing your expertise to this conversation. Thank you. It's great to |
| 1:57.9 | be here. I wanted to begin with something very familiar. |
| 2:02.8 | Anyone who has studied a bathroom floor or maybe wall tiles might have noticed that if they're made out of a single tile, |
... |
Please login to see the full transcript.
Disclaimer: The podcast and artwork embedded on this page are from Steven Strogatz, Janna Levin and Quanta Magazine, and are the property of its owner and not affiliated with or endorsed by Tapesearch.
Generated transcripts are the property of Steven Strogatz, Janna Levin and Quanta Magazine and are distributed freely under the Fair Use doctrine. Transcripts generated by Tapesearch are not guaranteed to be accurate.
Copyright © Tapesearch 2026.