Hello. I’m Christian Perfect and here are some more maths links, after an almost geological gap of one month and one day. I told you this wasn’t going to be a periodical!
There’s going to be some sexy maths at the bottom of this issue of the Aperiodical. I’m just letting you know now so you can prepare yourself by getting in an appropriate state of mind. Maybe some of the links on the way down there will help with that.
Mathematicians like counting. We like counting how many of a thing exist and how many ways a thing can be done and how many kinds of finite simple group there are. In much the same spirit, this happy lady enumerates in a very pleasing video the twenty-five ways she knows of wearing a scarf fashionably. Is this all of them? Are they all different modulo rotation and translation? I think these questions require rigorous mathematical analysis, hopefully in the form of more snappily-edited videos featuring smiling ladies.
OK, so it was a bit of a stretch to claim that video about scarves was also about maths. But this video contains both Leibniz and scarves, so you know it’s maths. It’s also really interesting on its own merits: it’s a presentation by someone who knits stories into scarves using Morse code.
What’s the biggest number of chicken nuggets that you can’t order at McDonald’s without wasting any? In the 1980s, the answer was 43.
McDonald’s is more interesting than that though. In the US they make a thing called the McRib, a sandwich whose appearances seem as transitory and unpredictable as those of the Virgin Mary or the English summer. This article at The Awl makes the case that McDonald’s uses the introduction of the McRib to influence the price of pork. With a graph! So it’s maths!
One final fluff link before we get into the real maths. Here’s a logic quiz that you are guaranteed to fail because of your own PERFIDIOUS BRAIN.
OK, enough weaksauce links and burgers! Time for real maths!
Sphere-packing is a little bit easier now (and here’s the arXiv paper for those who, like me, get nothing out of pop-science writeups and their awful “hey-I-can-relate-to-that-but-you-haven’t-really-made-the-story-any-clearer” way of analogising abstract results). That isn’t the real maths though: it’s imprecise fiddling by a physicist. Real mathematicians only recognise one kind of hard: NP-hard. And circle-packing is hard.
It’s December now, so you probably want to put up some Christmas decorations. Make mathematical ones! Math Craft, which has been aggregating some really good stuff on how to make mathsy objects since it opened recently, has got you covered. They’ve got instructions for six-sided paper snowflakes, an origami christmas tree and they link to a fun article about the fractal patterns you can find in Christmas tree baubles. They’ve got loads of other interesting stuff as well, and they seem to be posting pretty often, so do have a look around. If you’re thinking about making the Christmas tree, be warned: I got roped into an attempt to make it before a seminar on Thursday and it turned out to be way more effort than I thought it would be. I gave up and I feel no shame about that.
A while ago, the people who make episodes of Futurama made an episode of Futurama where everybody’s minds get swapped. One of the writers came up with a group-theoretic justification for the way they resolve the head-swapping. It was pretty fun, and generated quite a few popular maths pieces in the media. Dana Ernst has written a really fantastic set of slides to go with a talk about the episode and its maths. He uses all the trendy web technologies – embedded videos, MathJax, and so on. He even includes an interactive Sage input so you can play about with the groups involved yourself. This is the future of maths exposition!
My last bit of real maths is something I found via Jeff Erickson. It’s an essay on the topic of wooden train-track sets, answering the question of which layouts of left- and right-turning pieces construct a closed curve. It’s a piece of mathematics so beautiful that you will want to kiss your monitor. I’m going to print it out and give it to people I meet. I think I love it.