Note: If you’re looking for instructions on solving Rubik’s cube from any position, there’s a good page at Think Maths.
One day some years ago I was sat at my desk idly toying with the office Rubik’s cube. Not attempting to solve it, I was just doing the same moves again and again. Particularly I was rotating one face a quarter-turn then rotating the whole cube by an orthogonal quarter-turn like this:
Having started with a solved cube, I knew eventually if I kept doing the same thing the cube would solve itself. But this didn’t seem to be happening – and I’d been doing this for some time by now. This seemed worthy of proper investigation.
‘Tis the season to celebrate the circle constant! Yes, that’s right: in some calendar systems using some date notation, the day and month coincide with the first three digits of π, and mathematicians all over the world are celebrating with thematic baked goods and the wearing of irrational t-shirts.
And the internet’s maths cohort isn’t far behind. Here’s a round-up (geddit – round?!) of some of our favourites. In case you were wondering, we at The Aperiodical hadn’t forgotten about π day – we’re just saving ourselves for next year, when we’ll celebrate the magnificent “3.14.15”, which will for once be more accurate to the value of π than π approximation day on 22/7. (Admittedly, for the last few years, 3.14.14 and so on have strictly been closer to π than 22/7. But this will be the first time you can include the year and feel like you’re doing it right.)
Happy New Year! And welcome to the first Carnival of Mathematics of 2014. The Carnival is a monthly roundup of blog posts on or related to mathematics, from all over the internet. Posts are submitted by authors and readers, and collated by the host, whose blog it’s posted on. This month, the Carnival has pulled in here at The Aperiodical, and we’re all ready with our party hats for the celebration of mathematical blogging that implies.
Katie, one of our editors, has been contacted by Brendan with a question about some maths he’s been investigating. Read on to find out what he’s discovered, and read Katie’s response.
Dear The Aperiodical,
I’ve noticed an interesting property of numbers, and I wondered if you could tell me if this is something which is already known to mathematicians? I’ve been calling them Dual Inversal Numbers, but I’d love to know if they have an existing name, and if there’s anything else you can tell me about them.
In this short series of articles, I’m writing about mathematical questions we don’t know the answer to – which haven’t yet been proven or disproven. This is the third article in the series, and across two parts will discuss various open conjectures relating to prime numbers. This follows on from Open Season: Prime numbers (part 1).
So, we have a pretty good handle on how prime numbers are defined, how many of them there are, and how to check whether a number is prime. But what don’t we know? It turns out, quite a lot.
In this short series of articles, I’m writing about mathematical questions we don’t know the answer to – which haven’t yet been proven or disproven. This is the third article in the series, and across two parts will discuss various open conjectures relating to prime numbers.
I don’t think it’s too much of an overstatement to say that prime numbers are the building blocks of numbers. They’re the atoms of maths. They are the beginning of all number theory. I’ll stop there, before I turn into Marcus Du Sautoy, but I do think they’re pretty cool numbers. They crop up in a lot of places in maths, they’re used for all kinds of cool spy-type things including RSA encryption, and even cicadas have got in on the act (depending on who you believe).
Starting next week, the historic city of Edinburgh will be taken over by entertainers of all types, performing comedy, dance, theatre and music, entertaining visitors to their massive world-famous festival fringe. Since discerning mathematicians sometimes also enjoy being entertained, I thought I’d write a roundup of the shows maths has non-empty intersection with.
First up, since we haven’t mentioned him in a while, it’s Alan Turing! No, his reanimated corpse isn’t performing edgy stand-up, but theatre company Idle Motion is performing a visual theatre piece entitled That Is All You Need To Know, celebrating the work of Bletchley Park codebreakers. Alan Turing Alan Turing Alan Turing.