For a while, I’ve been following this cool Twitter account that tweets questions Wolfram|Alpha can’t answer. The genius of it is that the questions all look like things that you could half-imagine the solution algorithm for at a glance, and many of them look like the kinds of questions Wolfram like to give as examples when they’re showing off how clever their system is.
Questions like this:
The answer to that is 278. How do I know that? I know that because I went on a little problem-solving binge answering the questions that Wolfram|Alpha can’t.
Sam’s dad is in a mathematical conundrum – so she’s asked Katie, one of our editors, if maths can save the day.
Dear The Aperiodical,
My dad is going away on a golfing holiday with seven of his friends and, since I know a little bit about mathematics, he’s asked me to help him work out the best way to arrange the teams for the week. I’ve tried to work out a solution, but can’t seem to find one that fits.
They’ll be playing 5 games during the week, on 5 different days, and they’d like to split the group of 8 people into two teams of four each day. The problem is, they’d each like to play with each of their friends roughly the same amount – so each golfer should be on the same team as each other golfer at least twice, but no more than three times.
Can you help me figure it out?
Sam Coates, Manchester
Bees have encouraged mathematical speculation for two millennia, since classical scholars tried to explain the geometrically appealing shape of honeycombs. How do bees tackle complex problems that humans would express mathematically? In this series we’ll explore three situations where understanding the maths could help explain the uncanny instincts of bees.
A curvy wild honeycomb.
Honeybees collect nectar from flowers and use it to produce honey, which they then store in honeycombs made of beeswax (in turn derived from honey). A question that has puzzled many inquiring minds across the ages is: why are honeycombs made of hexagonal cells?
The Roman scholar Varro, in his 1st century BC book-long poem De Agri Cultura (“On Agriculture”), briefly states
“Does not the chamber in the comb have six angles, the same number as the bee has feet? The geometricians prove that this hexagon inscribed in a circular figure encloses the greatest amount of space.”
(A report by Richard Elwes from the launch of the London Mathematical Society’s 150th birthday year. All the talks are available to watch online at the LMS’ birthday portal)
There’s a standard format for celebrating a mathematical milestone, perhaps the 80th birthday of some deeply eminent number theorist. His collaborators and graduate students, and their graduate students, and their graduate students all gather together in some gorgeous location to regale each other with their latest theorems, while the rest of the world pays no attention. For the London Mathematical Society’s birthday, we had something different. Well, we did have the gorgeous location. The Goldsmiths’ hall in London is a magnificent venue, and the livery hall in particular was evidently designed by someone with a peculiar fondness for Element 79. (See for yourself.) But speaker-wise, a decision had obviously been taken that the party would be an outward-looking affair. The focus was not so much on the LMS, or even on maths per se, but on our subject’s ability to unlock worlds, particularly the worlds of TV, film, and computer games.
In an idle moment of wondering, I asked a simple question on Twitter:
The response was overwhelming. Here’s a guide to the non-existent number crunchers you should know about, and some you probably already do.
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 $82680$ cm3. How did they get that?
I decided to do some calculus of variations, or whatever it’s called.