I don’t know why this question popped into my head, but it’s been sitting there for the past week and showing no signs of moving on.

Suppose an enemy of mine threw a friendly blue whale at me. Being a friendly whale, it makes the blue-whale-noise equivalent of “DUCK!” to warn me it’s coming.

How quickly does the whale need to be travelling for its warning to be useful?

This article on BBC News caught my eye because it has “maths” in the headline. Yes, I’m that easily pleased.

Somewhere in the middle, it says that myHermes requires the “volumetric area” of a parcel to be less than 225cm. That’s right: the “volumetric area” is neither a volume nor an area but a length. Anyway, the formula for volumetric area of a package with sides $a,b,c$, where $a \leq b \leq c$, is

\[ 2(a+b) + c \]

(Importantly, $a$ and $b$ are always the two shortest sides of the package)

So the constraint is

\[ 2(a+b) + c \leq 225 \]

In the next paragraph is the puzzling statement that the maximum allowable volume for a package is $82.68$ litres, or $82680$ cm^{3}. How did they get that?

I decided to do some calculus of variations, or whatever it’s called.

The Imitation Game is the new film starring Sherlock Holmes as Benedict Cumberbatch as Alan Turing, and Keira Knightley as Kate Winslet as Joan Clarke. Together they are two mathematicians in World War II trying to build a bombe. The film will soon be available on DVD, blu-ray, and as an animated GIF set on tumblr.

“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.

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.

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.

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.