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Oh, Stephen

hawking penalty formula

“It is hugely complicated. In fact, compared to football I think Quantum Physics is relatively straightforward.”
– Professor Stephen Hawking

Even you, Stephen?

If you pick up basically any newspaper in Ireland or the UK today, you’ll probably find a story about Professor Stephen Hawking’s “formula for World Cup success”. At first glance, it doesn’t look good: The World’s Most Famous Scientist appears finally to have succumbed to the temptation of nonsense formula publicity.

Aperiodical Round Up 10: a rathole down which valuable mathematical effort is being poured

V0025329 A middle-aged man giving a geometry lesson to young woman, a

Ten! TEN! TEN! Incredible. David Cushing asked me a very good question once: what have you done between five and ten times (inclusive)? Well, this is the last time ‘Writing an Aperiodical Round Up’ will be in the same category as ‘getting a new wallet’ and ‘saying hello to Peter Beardsley’.

Hello, my name’s Christian Perfect and, more often than an unbiased observer would expect, I find odd maths things on the internet.

Poetry in Motion

Phil Ramsden gave an excellent talk at the 2013 MathsJam conference, about a particularly mathematical form of poetry. We asked him to write an article explaining it in more detail.

Generals gathered in their masses,
Just like witches at black masses.

(Butler et al., “War Pigs”, Paranoid, 1970)

Brummie hard-rockers Black Sabbath have sometimes been derided for the way writer Geezer Butler rhymes “masses” with “masses”. But this is a little unfair. After all, Edward Lear used to do the same thing in his original limericks. For example:

There was an Old Man with a beard,
Who said, “It is just as I feared!-
Two Owls and a Hen,
Four Larks and a Wren,
Have all built their nests in my beard!”

(“There was an Old Man with a beard”, from Lear, E., A Book Of Nonsense, 1846.)

And actually, the practice goes back a lot longer than that. The sestina is a poetic form that dates from the 12th century, and was later perfected by Dante. It works entirely on “whole-word” rhymes.

How to solve a Rubik’s Cube in one easy step

Note: If you’re looking for instructions on solving Rubik’s cube from any position, there’s a good page at Think Maths.

One day some years ago I was sat at my desk idly toying with the office Rubik’s cube. Not attempting to solve it, I was just doing the same moves again and again. Particularly I was rotating one face a quarter-turn then rotating the whole cube by an orthogonal quarter-turn like this:

Having started with a solved cube, I knew eventually if I kept doing the same thing the cube would solve itself. But this didn’t seem to be happening – and I’d been doing this for some time by now. This seemed worthy of proper investigation.

Carnival of Mathematics #106 – December 2013

Carnival of Mathematics LogoHappy New Year! And welcome to the first Carnival of Mathematics of 2014. The Carnival is a monthly roundup of blog posts on or related to mathematics, from all over the internet. Posts are submitted by authors and readers, and collated by the host, whose blog it’s posted on. This month, the Carnival has pulled in here at The Aperiodical, and we’re all ready with our party hats for the celebration of mathematical blogging that implies.

An enneahedron for Herschel

The building where I work is named after Alexander Stewart Herschel. I suspect this is because it used to be the home of the physics department, since he was an astronomer, but it works for us too because he also has a pretty cool graph named after him.

herschel graph

An embedding of the Herschel graph in the plane

Helpfully, it’s called the Herschel graph. It’s the smallest non-Hamiltonian polyhedral graph – you can’t draw a path on it that visits each vertex exactly once, but you can make a polyhedron whose vertices and edges correspond with the graph exactly. It’s also bipartite – you can colour the vertices using two colours so that edges only connect vertices of different colours. The graph’s automorphism group – its symmetries – is $D_6$, the symmetry group of the hexagon. That means that there’s threefold rotational symmetry, as well as a couple of lines of reflection. It’s hard to see the threefold symmetry in the usual diagram of the graph, but it’s there!

Anyway, at the start of the summer, one of the lecturers here, Dr Michael White, told me about this graph and asked if we could work out how to construct the corresponding polyhedron. Making a polyhedron is quite simple – take the diagram on the Wikipedia page, pinch the middle and pull up – but it would be really nice if you could make a polyhedron which has the same symmetries as the graph.