{"id":2228,"date":"2016-08-15T21:32:15","date_gmt":"2016-08-16T02:32:15","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=2228"},"modified":"2016-08-15T21:32:15","modified_gmt":"2016-08-16T02:32:15","slug":"carnival-of-mathematics-137","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2016\/08\/15\/carnival-of-mathematics-137\/","title":{"rendered":"Carnival of Mathematics 137"},"content":{"rendered":"

Welcome to the 137th<\/sup> Carnival of Mathematics<\/a>! 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<\/em>, but depending where their roller goes on any given day, you could end up with a different number of slices<\/em>.<\/p>\n

\"Here<\/a>

Here a lazy pizza cutter only got 9 pieces out of 4 cuts when he could have gotten 11. Shame.<\/p><\/div>\n

And this brings us to the number 137, which is the 16th<\/sup> lazy caterer number<\/a>. 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 16th<\/sup> smart pizzeria number. In general the nth<\/sup> lazy caterer number is given by the equation n^2+n+2<\/sup>⁄2<\/sub>, and together they form the lazy caterer sequence<\/p>\n

\n1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154,…\n<\/p><\/blockquote>\n

of which 137 is the 16th<\/sup> term (assuming we call 1 the 0th<\/sup> 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 nth<\/sup> lazy caterer number when they start slicing, y’know, just to make things fair. <\/p>\n

Now, on to the main dish of this carnival: the posts of the month! <\/p>\n