*Double Maths First Thing is, fundamentally, somewhere for Colin to dump all his open tabs.*

Hello! My name is Colin and I am a mathematician on a mission to spread mathematical mirth, geometric joy, and delight in the beauty of whatever this is. Let’s boogie.

### A bit random

Since I’m applying for a job that involves Monte Carlo methods — which I’ve seen described as “integration by darts” — I’ve been looking at computer-generated “randomness” this week.

Matt Parker, with a contribution from Grant Sanderson, has a video making sense of why taking the square root of a uniform random number gives the same distribution as taking the larger of two.

I’ve also stumbled on a way to make your random number generator faster, and a way to turn biased coins into fair ones — although I’m not aware that it’s possible to create an unfair one.

### Random, not random

Recent adventures in 3D printing had me thinking about how it’s possible to throw different shadows from different directions. Only tangentially related, you can use moiré effects to create weird (but useful) effects, such as signs for ships. There’s more about it in Chalkdust, which is a magazine for the mathematically curious. Issue 20 will be out at some point in the next month!

I never know quite what to make of Quanta magazine — sometimes it feels great, and sometimes it feels a bit patronising. It took quite a lot of reading to get to the point of this article, about multiple imputation in stats, but I still found it interesting.

If you’re interested in solving a Millennium Prize problem, you might start by reading up on what P vs NP is actually about. You lose a maths point if you say “P=NP iff N=1 or P=0.”

Lastly, I thought this piece about ‘mathiness’ — dressing nonsense up in mathematical clothes to fool people into thinking it’s sense — was excellent; not just describing the problem, but offering solutions too.

### A curiosity to end on

Lastly lastly, there is one Latin square of order 1, two of order 2, twelve of order 3… but it’s really hard to prove that it’s an increasing sequence. I thought that was interesting.

In the meantime, if you have friends and/or colleagues who would enjoy Double Maths First Thing, do send them the link to sign up — they’ll be very welcome here.

If you’ve missed the previous issues of DMFT or — somehow — this one, you can find right here at the Aperiodical.

That’s all for this week! If there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website. You can also just reply to this email if there’s something I should be aware of.

Until next time,

C