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Open Season: Pancake Flipping

In this 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 edition is a topical one, for Pancake Day (Shrove Tuesday, celebrated in the UK this year on 9th February).

pancakesSome of the best mathematical teasers are those which originate in a real-world problem – although the problem for pure mathematicians is that that happens much less often than it does for applied mathematicians, who are presented with interesting real-world problems all the time. That’s why it’s especially nice when a more pure one pops up, and that’s exactly what happened to mathematician Jacob E Goodman, back in 1975.

The Aperiodical’s Actual Snowflake Competition – Results

Before Christmas, we launched a winter-themed maths competition – to design a sensible hexagonal snowflake, using a square grid, which could be used to knit a wintery jumper and not a) look terrible or b) have non-hexagonal symmetry. We had a deluge of entries, some valid and others less so – in fact, we may have had at least one entry break each of the rules we set. Below is a round-up of all the entries we received.

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

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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

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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.