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Not mentioned on The Aperiodical this month, May 2016

Here are a few of the stories that we didn’t get round to covering in depth this month.

Turing’s Sunflowers Project – results

Manchester Science Festival’s mass-participation maths/gardening project, Turing’s Sunflowers, ran in 2012 and invited members of the public to grow their own sunflowers, and then photograph or bring in the seed heads so a group of mathematicians could study them. The aim was to determine whether Fibonacci numbers occur in the seed spirals – this has previously been observed, but no large-scale study like this has ever been undertaken. This carries on the work Alan Turing did before he died.

The results of the research are now published – a paper has been published in the Royal Society’s Open Science journal, and the findings indicate that while Fibonacci numbers do often occur, other types of numbers also crop up, including Lucas numbers and other similarly defined number sequences.

Maths Object: Nobbly Wobbly

My maths object this time is one of my dog’s favourite toys: the Nobbly Wobbly.

In the video, I said it was invented by a mathematician, but Dick Esterle’s bio normally goes “artist, architect, inventor”. I’ll leave it up to you to decide if Everyone’s a Mathematician.

It’s a particularly pleasing rubbery ball thing made of six interwoven loops in different colours, invented by Dick Esterle.

On Google+, various people told me the unexpected fact that the outer automorphism group of $S_6$ is hiding inside this dog toy.

I’ve also found this Celebration of Mind livestream starring Dick Esterle from 2013 talking about all sorts of mathematically-shaped toys, including the Nobbly Wobbly.

Are you sure 51 isn’t prime? – Analysing the results of the “Is this prime?” game

Two months ago, I bought isthisprime.com and not only set up the internet’s fanciest primality-checking service, but also invented a rather addictive game.

It quite quickly went viral, or as relatively viral as a maths game can get, with people tweeting their high scores and posting the link to reddit and Hacker News. I realised fairly soon that I should put in some stats tracking, to see if there were any interesting patterns in the data (and also to inflate my ego as the “games played” counter went up). I missed the first big spike in traffic, but on the 9th of March I wrote a script which saved a record of each game to a database.

isthisprime game dates

The mad rush settled down quite quickly but there were still occasional spikes as different sites or people with lots of twitter followers found the game. Now, after two months, I’ve got data for just under 350,000 games. That’s a decent amount of information!

Ever been involved in publishing research? Answer this survey of mathematical publishing priorities

From Mark C. Wilson of the University of Auckland, a little public service announcement for anyone who’s ever been involved with a mathematical journal.

Dear colleagues,

There is much dissatisfaction with the current state of research
publication, but little information on community attitudes and priorities.
I have started a survey which I hope you will fill in (I estimate 10-15
minutes, and it is completely anonymous). The results will be made publicly
available later this year. I hope that it will help to focus our efforts as
a community by allowing us to work toward broadly agreed goals.  I want to
get as representative and as large a sample of the world mathematical
community as possible. Please forward to your  local colleagues.

Please answer this  survey if and only if you have been involved with a
mathematical journal as editor, reviewer/referee, author or reader in the
last 3 years. By “mathematical” we also mean to include theoretical
computer science and mathematical statistics journals, and disciplinary
journals used by applied mathematicians. Essentially, any journal covered
by Mathematical Reviews qualifies.

Answer the survey

Kickstart the Mandelmap poster: a vintage style map of the Mandelbrot set

Here’s something fun you might want to spend some money on: a poster of the Mandelbrot set, in the style of an old-fashioned navigation chart.

The Kickstarter has already racked up many multiples of the original funding goal with three weeks still to go, so it’s at the “effectively a pre-order” stage. The posters start at \$26.

Kickstarter: Mandelmap poster by Bill Tavis.

Steinberg’s conjecture is false

Conjecture   Every planar graph without 4-cycles and 5-cycles is 3-colourable.

Nope!

In a paper just uploaded to the arXivVincent Cohen-Addad, Michael Hebdige, Daniel Kral, Zhentao Li and Esteban Salgado show the construction of a graph with no cycles of length 4 or 5 which isn’t 3-colourable: it isn’t possible to assign colours to its vertices so that no pair of adjacent vertices have the same colour, using only three different colours. This is a counterexample to a conjecture of Richard Steinberg from 1976.

The problem was listed in the Open Problem Garden as of “outstanding” importance.

Read the paper: Steinberg’s conjecture is false

via Parcly Taxel on Twitter

Approximate a ratio by folding a piece of paper

towel-ratio

Warning: you could make a very strong argument I’ve thought far too much about something inconsequential. If that makes your stomach turn, look away now.

This morning in the shower, I had an idle thought about my towel. It was, as always, folded neatly on the toilet seat. A problem that’s been bugging me for a few days is how to pick up the towel by a section of the long edge, so when it unfolds it’s the right way round.

* quiet in the back

The problem is that the short edge and the long edge look the same, and once I’ve folded the towel over a couple of times and had a shower only a madman* would remember which is which. But my towel isn’t square, so it occurred to me that either the longer or the shorter edge, after folding, could be the edge I want. Since I never make a diagonal fold, the long edge is only ever folded on top of the long edge, and likewise for the short edge. I fold the towel until it fits comfortably on top of the toilet seat, and by the time I’ve finished my shower I can’t be relied upon to remember which sequence of folds I did.

Which got me thinking about the ratio between the width and height of my towel: if I know this ratio then, by looking at the towel and counting the number of folds, I can work out which folds I’ve done, and hence which of the sides will unfold to be the long edge.