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Kevin Knudson: Welcome to My Favorite Theorem, the math podcast with no quiz at the end. I'm Kevin Knudson, professor of mathematics at the University of Florida and I am joined as always by my fabulous other host, co-host? I don't know,



Evelyn Lamb: Co-host. It’s a host but going in the opposite direction.




KK: That’s right. We reverse the arrows. Haha, math joke.




EL: Yes, I'm Evelyn Lamb, a freelance math and science writer in Salt Lake City, Utah. Actually just got back to Salt Lake from a wonderful trip this past week where I got to meet two new additions to my family, ages three months and three weeks. So that was, that was pretty fun, to hold one of the tiniest babies I've ever held. So yeah, very nice little fall trip to take. And now I'm back here and talking about math.




KK: Yeah, well, last Friday night, I drove two hours over to Ponte Vedra, which is sort of near Jacksonville, by myself to a concert. So this is where I am in life. So I went to see Bob Mould, who many people may or may not know, but he was — Yeah, Christopher's shaking his head yeah. He was at Hüsker Dü and then Sugar. He's been doing solo albums forever. And I've been a fan for going on 40 years, which is also weird to say. Had a great time, though. By myself, that's great. This is what one does in his 50s I suppose. Anyway, not as exciting as holding a newborn but, but still pretty good. So anyway, hey, let's talk math. So today, we are pleased to welcome Christopher Danielson to the show. Why don’t you tell us about yourself.




Christopher Danielson: Yeah, I am coming to you from St. Paul, Minnesota.




KK: Nice.




CD: Bob Mould, also a fellow Minnesotan. [Ed. note: Bob Mould is actually from upstate New York.]




KK: He went to McAllister, right. Yeah.




CD: Nice. Right up the street from where I'm standing right now. I work a day job at Desmos Classroom, which is now part of Amplify, designing — working with a number of colleagues to design math curricula. We are currently working on an Algebra I curriculum, about to wrap that up, and moving on to Geometry. And then on the side, I have many projects, some of which will come up in our work today. But I think I understand that you two are familiar with the Talking Math With Your Kids blog that grew into then a large-scale playful annual family math event at the Minnesota State Fair called Math on a Stick.




KK: Cool.




CD: And I also am Executive Director at a small nonprofit that seeks to create playful, informal math experiences for children and families in the same spirit as the work we do at Math on a Stick, but designed for a variety of other sorts of spaces. That nonprofit is called Public Math.




KK: Very cool.




EL: So I'm probably doing that thing where I generalize from a small number of examples. One of my best friends in grad school was from Minnesota, and just loved the State Fair. So I think that Minnesotans just have it this special relationship with the State Fair. And so I did — I am really interested in hearing more about how you do Math on a Stick at the Minnesota State Fair.




CD: Yeah. Should I pick that up right now? Or is there more on the agenda?




EL: Yeah, that would be great!




KK: No, go ahead.




CD: Yeah, so the Minnesota State Fair, it's the second largest state fair in the country behind only of course, Texas.




EL: Where I am from.




CD: Oh, nice. Texas lasts for a month. Ours is 12 days. 12 days of fun ending Labor Day is one of the mottos. The other is the great Minnesota get-together. The location of the fairgrounds is especially convenient for large attendance. The fairgrounds are right, sort of on the border between Minneapolis and St. Paul. And they have been, for probably the past 20 years, have been working on developing some educational and family friendly spaces, out of a perception that it is expensive to go to the fair, which is true, but then once you're in that there isn't much to do besides look at animals and buy a bunch of food.




EL: On a stick.




CD: Yeah, on a stick. So they’ve been working on that. And that led to a lovely literacy space called the alphabet forest that is about 12 years old now. And the first time I sat down there, it was their fifth year and was like the sky, the clouds parted and the angels sang, and I was like, I’ve got to figure out how to build a math version of this. And so together with some organizational support from the Minnesota Council of Teachers of Mathematics and a bunch of expertise from folks that I know through the blog work and through my work in math education, put together a pitch, and after many very boring meetings, it became a thing. So we've got about 15 to 20, different mathematical, playful, creative math activities, everything from a big table full of tiling turtles, to a set of numbered stepping stones that you just see kids jumping up and down happily counting, counting by twos, creating all sorts of fun things to do with. We have a different visiting mathematician or mathematical artist every day, each of the 12 days and they bring whatever sort of hands-on thing they're into. Sometimes that's sort of the standard stuff with, like, Mobius strips and hexaflexagons, and sometimes it is new and new and delightful, creative things that the world has never seen before. So yeah, Math on a Stick, come on out and play with us. 12 days of fun ending Labor Day, always starts on a Thursday, runs through a full week, two weekends and then ends on Monday.




EL: Yeah, that does sound like a neat thing. Sometimes I go to the farmers market here or something like that, and I just think, like, where are there opportunities to kind of create, like you said, these playful, you know, a non-classroom math experience for people?




CD: Yeah, my, one of my Public Math colleagues has a project called Math Anywhere, Molly Daley. She's in Vancouver, Washington, and also does some stuff across the river in Portland, Oregon. And farmers markets are one of the more successful spaces for her. So she'll pay for, for a booth, she has grant money, she'll pay for a booth and just set up a much smaller version of Math on a Stick stuff, as well as some other stuff that she's designed or harvested from other places, but three or four activities, and yeah, delightful times ensue. However, I had a recent experience at the Mall of America, largest shopping complex, also here in the Twin Cities. And it was really interesting, because the way that kids’ families move through the Mall of America is wildly different from how they move through the state fair. So just an invitation to a big STEM/STEAM carnival. And we brought some — one of our favorite things is called a pattern machine or punchy buttons, a nine by nine grid of punchy buttons that you can drop pictures on. And each button is clicky and on a ballpoint pen. So we bought a bunch of those. And then we also had the mega pattern machine, which is just thousands of buttons from all these machines smashed together to make a nice big floor space. But the way that kids come into Math on a Stick is that there’s, like, this long elastic band between parents and children at the fair, not in the super crowded spaces in the fair, but in the less crowded spaces. And so often kids will see those stepping stones that, by the way, start at zero, and then continue on to 23. Yeah, so they'll start on the zero, and they'll lead the way into the space, like we deliberately set up those stepping stones to that the edge of this outdoor space. And by the time kids get to 23, now they're surrounded by eggs that they can put into — little plastic eggs they can put into large egg crates, and tiling turtles and pattern machines and all sorts of fun things to do. And families will sort of follow along behind. At the mall, there’s none of that. There's none of that. Families move in really tight units. There's no, like ,a child leading the family into a space, which is just a really interesting dynamic. And having been out in Portland a couple of weeks ago with Molly when she was at one of the farmers markets, it felt very much more like the fair. A mom or a dad might be much more likely to say, okay, sweetie, you keep playing with these turtles, I'm going to hop over there and buy some apples and I’ll be back in two minutes. They kind of keep their eye on them and everything, but that that elastic band is much longer. Nobody ever says, okay, sweetie, you know, their four year old, I'm going to I'm going to just hop across to, you know, the department store over here, you keep playing with something in the hallway. So Public Math is our project where we're trying to think about how do you design for those kinds of spaces? What would have been a better design than the one we had for something like them our time at the Mall of America?




EL: Yeah. Interesting different kinds of math problems to solve. Different optimization.




KK: That’s right. Yeah. All right. So this podcast does have a name, though. So presumably, you have a favorite theorem. So you want to tell us what it is?




CD: I do! And it is — Yeah, my favorite theorem is, I'll state it simply. And then I guess we get to talk about like, why it’s my favorite and things?




KK: Yeah, sure.




EL: Yeah.




CD: It doesn't have a name. I feel like maybe, maybe it should have — maybe it has a name. Maybe you'll know a name for well,




EL: We’ll brainstorm about it.




CD: But yeah, let me state it simply, which is that t