How many ways to shuffle a pack of cards?

This is an excerpt from friend of The Aperiodical, Matt Parker’s book, “Things to Make and Do in the Fourth Dimension”, which is out now in paperback.

9780141975863

There’s a lovely function in mathematics called the factorial function, which involves multiplying the input number by every number smaller than it. For example: $\operatorname{factorial}(5) = 5 \times 4 \times 3 \times 2 \times 1 = 120$. The values of factorials get alarmingly big so, conveniently, the function is written in shorthand as an exclamation mark. So when a mathematician writes things like $5! = 120$ and $13! = 6,\!227,\!020,\!800$ the exclamation mark represents both factorial and pure excitement. Factorials are mathematically interesting for several reasons, possibly the most common being that they represent the ways objects can be shuffled. If you have thirteen cards to shuffle, then there are thirteen possible cards you could put down first. You then have the remaining twelve cards as options for the second one, eleven for the next, and so on – giving just over 6 billion possibilities for arranging a mere thirteen cards.

Mathematical Scarves Kickstarter

If you like your accessories ‘provably unique’, check out this mathematically interesting Kickstarter project – KnitYak, aka Fabienne Serriere, is going to generate some knitting patterns for scarves algorithmically, so no two scarves will be the same. They’ve hacked a knitting machine to use cellular automata to generate unique black-and-white patterns, which will be knitted in merino wool using a Jacquard (double) knit, resulting in lovely well-finished pieces by the sound of things (although the scarves start from $150, so you’d expect something pretty nice).

Check out the video below, and consider chucking some money on the KnitYak Kickstarter page.

The Amazing World of MC Escher

M.C. Escher, not the DJ but the Dutch graphic artist, is well known as being hugely influenced by mathematics. His woodcuts, lithographs and mezzotints (me neither) contain everything from warped perspective and optical illusions that play around with notions of distance and space, to beautiful tilings and tessellations with a distinctly mathematical flavour.

The first major UK show of Escher’s work has been put together by the Scottish National Gallery of Modern Art, in Edinburgh, and includes nearly 100 works from the collection of the Gemeentemuseum Den Haag in the Netherlands. It will be on display at the Scottish National Gallery from 27 June to 29 September, after which it’ll move to the Dulwich Picture Gallery in London from 14 October through to 17 January.

Both exhibitions have an entry cost, although there’s also a free event taking place at the Scottish National Gallery on 27 August, in which mathematician Professor Ian Stewart will talk about the mathematics in Escher’s work, apparently ‘in simple non-technical terms and with many illustrations’ (because people who go to art galleries presumably wouldn’t like it otherwise).

More information

The Amazing World of MC Escher, 27 June to 29 September, Scottish National Gallery of Modern Art

Event – Escher: A Mathematician’s Eye View, Prof. Ian Stewart, 27 August, Scottish National Gallery of Modern Art

MC Escher, 14 October to 17 January 2016, Dulwich Picture Gallery

Registration for the 2015 MathsJam conference is now open

Photo credit: Dave Hughes

Photo credit: Dave Hughes

The MathsJam annual conference is a magical time when maths geeks converge on a conference centre in the middle of nowhere near Stone and spend a weekend sharing their favourite puzzles, games, and mind-blowing maths facts.

Registration for the 2015 weekend, taking place on 6-7 November, has now been opened. More information about the conference, and how to register, can be found on the MathsJam Conference website.

We’ll all be there: join us!

UK National Lottery: now 21% more balls (rounded up)

This week, it was announced that from October the UK’s National Lottery, currently operated by Camelot and already providing a veritable Merlin’s cave of probability lessons for maths teachers, will be changing the rules for its main ‘Lotto’ draw. The main changes are that a new £1m prize will be added to the raffle element you didn’t know already happens, and that matching two balls will win a free ‘lucky dip’ ticket in the subsequent draw. The fixed £25 prize for matching three balls remains on the round table (even though it sometimes causes hilarious number gaffes).

But the Sword of Damocles hanging over Camelot’s changes is that there will be an extra ten balls to choose six from (59 instead of 49), dramatically lengthening the odds of winning all of the pre-existing prizes. This is our round-up of the media’s coverage of this mathematical “news”.