Welcome to the 137^{th} Carnival of Mathematics! Let me begin with a story about pizza. I was at one of my favorite pizzerias in New Haven recently where they have the craziest method for slicing pizza: start with a standard round pie, then just go at it with a pizza roller like a maniac, hacking it up willy-nilly. First, this is actually a really great way to slice a pie, because pizza is way better when you don’t have to commit to an entire slice. Second, it struck me as a risky move, since it’s really hard to guarantee that each customer is getting the same number of slices. Sure, they slice it the same number of *times*, but depending where their roller goes on any given day, you could end up with a different *number of slices*.

And this brings us to the number 137, which is the 16^{th} lazy caterer number. It’s the maximum number of pieces that you can get from cutting a circular pizza straight through 16 times — so really they should call it the 16^{th} smart pizzeria number. In general the n^{th} lazy caterer number is given by the equation ^{n^2+n+2}⁄_{2}, and together they form the lazy caterer sequence

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154,…

of which 137 is the 16^{th} term (assuming we call 1 the 0^{th} term). So those pizza cutters at my pizzeria should go on doing exactly what they’re doing, but always be sure to aim for the n^{th} lazy caterer number when they start slicing, y’know, just to make things fair.

Now, on to the main dish of this carnival: the posts of the month!

- I really liked this piece from Brian Hayes about the derivation of wire gauging. Seriously, before today I had spent approximately 0 minutes of my life talking about gauged wires, but this post is so much fun I just made my poor mother listen to me explain to her all about 36 gauge wire and the 39
^{th}root of 92. Trust me, just go read it. - Kevin Knudson sent us a great piece about visualizing music mathematically. He describes a software that interprets the different tonal and percussive qualities of music to plot out a multidimensional character profile. I can’t get the real time video to load, but the still photos are already really cool. Plus, Michael Jackson.
- On the more technical end of things, a post from Mark Dominus explores how to decompose a function into its odd and even parts. It would be a fun discussion to have in an algebra or calculus class someday, I also like that Mark explains one piece of his discussion by saying “…as you can verify algebraically or just by thinking about it.” Ah, the old proof by just thinking about it trick.
- Gonzalo Ciruelos explains an algorithm for determining the roundest country. Harder than it sounds, and also, geez, the island nation of Nauru is really round. Check out the post for a ranking of the roundest countries.
- In case you’re wondering what’s going on with the ABC conjecture, this post from David Castelvecchi gives us a nice plain English update on what the key players in the fight to verify Mochizuki’s proof are up to these days.
- And for the crafty maker types, Nancy Yi Liang submitted this how-to guide for an incredible laser cut dress. The dress is a graphical visualization of some arcsin functions, and it’s custom made to fit!

Thank you for so many wonderful submissions! You can check information on past and future carnivals at The Aperiodical.