I recently heard about Herman, the German Friendship Cake (bear with me), a cake which is divided and spread among friends, and it got me thinking about some other foodstuffs I’ve heard of which are made in such a way that the amount you have will grow exponentially. A Herman cake is a special type of sourdough cake which is made with yeast. It’s explained fully here, but the idea is that you start with a solution of yeast, which lives in a little milk, sugar and flour. This small amount of goo can live happily at room temperature on a shelf, and if you stir it every day and give it a little more flour and sugar to eat every few days, after ten days it’s ready to make into a cake.
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I recently got a new set of business cards printed. I wanted to keep them as simple as possible, and have them communicate only the important information – my name and contact details. But then came the question of what to put underneath my name. I don’t currently have a full time job anywhere, but I do spend pretty much all my time working freelance as a maths communicator, talking to people about maths and popularising the subject. I also do loads of maths related things in my spare time, including running a Maths Jam, and I’m still in the process of writing a paper based on the work I did in my PhD thesis, which I finished last summer. How do you sum that up? I recall recently our own Peter Rowlett struggled similarly when filling in the corresponding field on his census form.
For the April 2012 issue of Puzzlebomb, I devised Hilbert’s Space-Filling Crossword:
The five clues lead to four four-letter words along the rows of the grid, and one sixteen-letter word snaking round the shape given by the thick lines. The puzzle gets its name from the shape traced out by the long word, which is the second iteration of Hilbert’s space-filling curve.
In my capacity as someone who occasionally turns up and does maths at people, I often find myself exposed to ‘starter puzzles’ – things the organisers provide to whichever group of humans have come to see me do maths, to give them something to do in any waiting time before the event starts. This is, of course, a fantastic source of ideas for the MathsJam I run in Manchester, as well as just being great for me as I get to have a go at them all.
One would be hard put to ﬁnd a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery — and more totally useless — than the perfect numbers.
— Martin Gardner
There are countless ways to classify integers. Happy, perfect, friendly, sociable, abundant, extravagant, cute, interesting, frugal, deficient, hungry, undulating, weird, vampire… the list goes on. But how useful are such classifications, beyond their inherent interestingness, and as a hook to get people into number theory?
A classic maths puzzle involves a line of one hundred prisoners, who have each been given a black or white hat by their nefarious captor, and must each correctly shout out the colour of their hat to win freedom. The twist is that the prisoners don’t know the colour of their own hat, and though they can see the colours of the hats in front of them, they don’t know many of each colour there are overall. They can confer on a strategy beforehand, and the aim is to get as many of them to correctly identify their hat colour as possible. You can find a full explanation here (and in many other places!)
There are several ‘sequels’ to this puzzle, some involving an infinite number of prisoners and requiring the axiom of choice to solve. This post is about a nice variation on the theme that I heard about at a recent MathsJam. It can (just about) be solved without knowledge of higher mathematics, and though it seems impossible at first glance, the prisoners in this situation can in fact save themselves with 100% certainty.
Science Showoff is a monthly night which takes place in a pub in London, and features acts from all areas of science, who each have 9 minutes to perform an act – a science demo, a routine, songs, experiments – anything entertaining or fun. Having tried a little bit of the short-set, trying-to-be-funny type of science communication involved in Bright Club (a similar venture, giving researchers the chance to try stand-up comedy, which started in London and has now spread all over the country), I thought it would be good to give it another go – in fact, Science Showoff was recommended to me by someone who saw my Bright Club set in Manchester. I had prepared an 8-minute piece about Fibonacci numbers to perform in Manchester, inspired by my artist friend’s admission that she didn’t see how maths could be interesting in the same way as art; she wasn’t there to watch, but I went down well (and ran horribly over time). So I decided to reprise my set at Science Showoff in February 2012 – and this time it would be the right length, and would be new and improved with all the best jokes left in and the duds taken out.