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Watch out! I’m a blue whale and I’m about to land on you!


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?

Apparently I’m not a maths genius (or, On the Subject of Parcel Sizes)

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 $82680$ cm3. How did they get that?

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

The conclusions you can draw from this graph will SHOCK you

This is a blog post based on a Google+ post about a tweet. I can only hope that it will inspire a further flourishing of vines, instagrams and Yo!-s.

I saw this graph (originally from job stats site posted by a functional programming news site:


The accompanying tweet said

“More reasons to choice Functional Programming – #Clojure and #Haskell highest paying #engineer salaries!”.

Well, should I “choice” Haskell or Clojure, based on the evidence in this graph?

Integer Sequence Review – Sloane’s birthday edition!

The Online Encyclopedia of Integer Sequences contains over 200,000 sequences. It contains classics, curios, thousands of derivatives entered purely for completeness’s sake, short sequences whose completion would be a huge mathematical achievement, and some entries which are just downright silly.

For a lark, David and I have decided to review some of the Encyclopedia’s sequences. We’re rating sequences on four axes: Novelty, Aesthetics, Explicability and Completeness.

CP: It’s Neil Sloane’s 75th birthday today! As a special birthday gift to him, we’re going to review some integer sequences.

DC: His birthday is 10/10, that’s pretty cool.

CP: <some quick oeis> there’s a sequence with his birthdate in it! A214742 contains 10,10,39.

DC: We can’t review that. It’s terrible.

CP: I put it to you that you have just reviewed it.

DC: Shut up.

CP: Anyway, I’ve got some birthday sequences to look at.

DC: About cake?

CP: No.

Diaconis-Mosteller approximation to the Birthday problem function.

1, 23, 88, 187, 313, 459, 622, 797, 983, 1179, 1382, 1592, 1809, 2031, 2257, 2489, 2724, 2963, 3205, 3450, 3698, 3949, 4203, 4459, 4717, 4977, 5239, 5503, 5768, 6036, 6305, 6575, 6847, 7121, 7395, 7671, 7948, 8227, 8506, 8787, 9068, 9351

James Grime’s house-building problem

Aperiodipal James Grime has put a new video on his YouTube channel. He’s got a problem to do with building houses:

[youtube url=]

But James posts fantastic videos about maths puzzles all the time; what’s so notable about this one?

I was involved, that’s what! The puzzle can be done on pen and paper but it involves a lot of drawing and calculating, so James asked if anyone could make a computery version. I spent my day off work last week making just such a thing: the computerised Building Houses Problem.