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Christmas Symme-tree

Christmas wrapping paper is sold in thousands of different variations, including plain, coloured, patterned, foiled and even flock, but one thing it’ll have in common is that it will repeat whatever pattern it has, regularly across the design.

I’m interested in symmetry, and was intrigued to find a curious fact about the symmetries of such repeating patterns – their symmetries are quite limited.

Tiling a finite plane


One of the many jobs we’re gradually getting round to in our new flat is that of tiling a small section of the kitchen surface, which for some reason was left blank by the original builders and all intervening owners. And what better thing to tile it with than binary numbers?

Review: Snowflake Seashell Star, by Alex Bellos & Edmund Harriss


Snowflake Seashell Star is a new mathematical colouring book, by Alex Bellos and Edmund Harriss, aimed at the lucrative ‘grown-up colouring books’ market that’s sprung up recently, heavily intersected with people who are interested in maths – the book can be used as a regular colouring book, but contains lots of interesting mathematical things, and mathematicians will love it. I wouldn’t have expected anything less from maths adventurer Bellos and mathematical artist and tiling fan Harriss, whose personalities both come through in the book – from the beautiful illustration to the playful style (and there’s a sneaky Harriss Spiral in there too).

The first thing I did in order to properly review the book was check an important mathematical fact, in case anyone was worried. And yes, everything in it is colourable using four colours or fewer. Phew.

New York Times puzzle is pure game theory

Image CC-BY Raymond Bryson, f-oxymoron on FlickrThe Upshot is a column in the New York Times based around analytics, data and graphics. (It was conceived around the time when Nate Silver left to work for ESPN). Earlier this week, managing editor David Leonhardt and data journalist Kevin Quealy posted an interesting puzzle, entitled ‘Are You Smarter Than 49,485 other New York Times Readers?’

The puzzle consists of a simple question – you need to pick a number between 0 and 100, and all 49,485 of the responses will be collated (assuming that every single one of the Times’ readership actually enters a number) and averaged. If your guess turns out to be the closest whole number to two-thirds of the average guess, you are clever and you win.

New pentagonal tiling discovered

If you’re into tilings, or just looking to redo your bathroom in the most modern way possible, there’s big news. A team of researchers at the University of Washington-Bothell have discovered a previously unknown way to tile a plane using irregular pentagons.

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”.