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Announcing the Big Lockdown Math-Off

The Big Lock-Down Math-Off

I don’t know about you, but right now maths is serving as a happy distraction from what’s going on outside. (You are inside, aren’t you?)

If there wasn’t currently a pandemic on, right now I’d be starting to think about how this year’s Big Internet Math-Off would run. Instead, I’ve had an idea: let’s have fun talking about interesting bits of maths now.

So, I’ve had an idea: the Big Lock-Down Math-Off. It’ll run like this:

  • Anyone who wants to take part, can.
  • Send in your pitch for a bit of fun maths.
  • I put all the pitches I receive in a pile
  • Each day, I pick two pitches off the pile, put them on the site and pit them against each other.
  • Everyone votes on the bit of maths that made them go ‘Aha!’ the most.
  • This continues until I run out of pitches, or we’re allowed outside again.
  • At the end, everyone wins.

I’ve already been in touch with some past Math-Off contenders, and it seems there’s some appetite for distracting ourselves with mathematical enthusiasm. I’d been low-key worrying about how to run this year’s tournament and who to invite, so I think I’ve solved a couple of problems here.

For this to work, I need two kinds of people:

Contenders

If you’ve got the time and mental bandwidth to make a pitch for a bit of maths that you enjoy, please do!

Your entry should be a pitch for the topic you’re proposing. It can include text, pictures, a video, links to resources, anything that can go in a blog post. You can include stuff that you haven’t made, or stuff that you’ve already put out on the internet; if you just add a sentence saying why you think the thing is cool, that’s fine. Enlisting the help of others to make your pitch is fine. I don’t want a lecture, or a wall of introductory lemmas – handwaving, and linking to deeper explanations, will make it more approachable.

Once you’ve made your pitch, send it in to upload.aperiodical.com. You can upload whatever files you like there, and I’ll see them. Please include whatever identifying information you’re willing to give. Anonymity is fine: I’ll make sure pitches by anonymous entrants only go up against other anonymous pitches.

You can submit more than one pitch, and there’s no deadline: we’ll keep adding pitches to the queue after the Math-Off has started.

If you make a video, please don’t upload it to us! Instead, put it on your own YouTube account (or whatever service you prefer) and send in a document with the link to the video.

For text, a Word document is fine, as is LaTeX.

Helpers

After last year’s tournament, a few people offered to help with admin for the next round. This year, I can use your help!

I’ll need people to help with transferring pitches from the drop-box to the Aperiodical’s editor, and setting up the polls.

If you’d like to help, please email root@aperiodical.com and I’ll give further instructions. Helpers can still make pitches – I’m planning on making a pitch or two myself.


The Big Lock-Down Math-Off will begin once I’ve got about 10 pitches. So get cracking!

Richard K. Guy (1916-2020)

Richard K, Guy

We’re greatly saddened to hear of the death of Richard K. Guy yesterday morning. He was 103.

Richard K. Guy was a prolific collaborator. He co-authored four papers with Paul Erdős, worked frequently with John H. Conway and Elwyn Berlekamp, and was a frequent contributor to Martin Gardner’s Mathematical Games column.

The most well-known of Guy’s discoveries is the glider in Conway’s Game of Life.

He described himself as an amateur mathematician, often tackling problems that are best described as ‘recreational mathematics’. His work was not restricted to one area of maths, but often involved a combinatoric aspect.

Recreational mathematics occupied Guy’s mind for much longer than a normal lifetime, so you’ll have to take your pick from his bibliography. Fortunately, many of the problems and ideas that Guy wrote about can be tackled independently. The Nesting and Roosting Habits of the Laddered Parenthesis and The Number-Pad Game are two typical examples.

Two of the most approachable of Guy’s books are Winning Ways for Your Mathematical Plays, written with John H. Conway and Elwyn Berlekamp, and The Book of Numbers, written with John H. Conway.

We wrote a post on Guy’s 100th birthday, and the University of Calgary set up a page celebrating his life. Colm Mulcahy also wrote a long post summing up Guy’s first 100 years in his MAA blog.

Guy’s final book, The Unity of Combinatorics, co-authored with Ezra Brown, is due out in May from MAA Press.

Where could you (or your rich pal) give everyone $1 million?

Recently someone on Twitter, and then two people on US cable news, said that Michael Bloomberg could have used the \$500 million he spent on his presidential campaign to give everyone in the USA \$1 million. This caused quite a fuss.

In short, someone divided 500 by 327, saw that the answer was bigger than 1 and the units were “millions”, and concluded that the money could instead have been distributed to give everyone \$1 million.

That’s an easy mistake to make for someone writing a tweet, but the kind of error that should have made someone think “does that make sense?” before planning a segment on TV news about it.

It’s raised a couple of interesting questions, though:

  • If that money was shared between every American citizen, how much would each one get?
  • If Michael Bloomberg wanted to give \$1 million to everyone in a smaller area, where could he choose?

I realised that all the data I need is freely available on the internet, so I made a website to do the calculations for you:

make-it-rain-bloomberg.glitch.me

It asks you how much money you’ve got, then for every power of 10 dollars, it tells you where in the USA you could give every resident that much.

To give you an idea of how far the net worths of people like Michael Bloomberg could go, it’s got a list of shortcuts for billionaires. Appropriately, I got that data from Bloomberg’s own website. Bloomberg himself was mysteriously missing from the list, so I got his net worth from Google and added it in myself.

The most unexpected thing for me was seeing how much money these people would have left over after giving everyone in the USA \$100. They’d still be enormously, unimaginably rich!

I’ll describe a few of the fiddly details of the implementation now. At first the “how much money have you got?” input was a text field, but I realised it’d be much better to have a slider that you can swing from \$1 all the way up to \$1 trillion. It’s a logarithmic scale, so powers of 10 are equally spaced.

I got data on the populations of US cities and states from data.census.gov.

Working out which amounts and places to show you wasn’t completely straightforward. I thought it’d be easiest to fix the amounts given away to a power of 10 per person, and to find places where the population meant that the amount left over would be as small as possible. To do that, my code works through the list of places in ascending order of population, and stops at the last place whose population is big enough to give everyone at least the target amount.

I enjoyed making this tool, and I hope it helps somebody get a better feel for what these big numbers mean.

Spread your wealth at make-it-rain-bloomberg.glitch.me.

SAMDOB – mess up the order of operations

While I’m on strike, I’m catching up on stuff I’ve made but never posted about here.

At the Talking Maths in Public conference last August, I was talking with Katie Steckles and Kevin Houston about the order of operations. I think that another one of those ambiguously-written sums had gone round Twitter again. I said it would be good to have a tool where you can write an expression, then change the order of operations and see what happens.

So, on the way home, I wrote one! I’ve called it SAMDOB, which is an anagram of BODMAS.

Screenshot of SAMDOB, showing the order of operations BO(DM)(AS) on the expression 2*3/3*2+2, which evaluates to 6
Screenshot showing how with the order of operations BOMD(AS), the expression evaluates to 3
Screenshot showing how with the order of operations BO(AS)(MD), the expression evaluates to 8.

Please have a play with it. I can imagine that this could be useful to people teaching the order of operations in real life. Let me know if you have any suggestions for improvements.

The code is on GitHub.

A paper version of the Seven Triples puzzle

Last year I wrote about a 3D-printed puzzle I’d designed, called Seven Triples.

At work we want to use this puzzle during an A-Level enrichment day, which means we need about twenty copies of it. I 3D-printed four copies over the course of a couple of weeks, in amongst other jobs, and I don’t have the patience to do any more. So, I’ve made a 2D version that we can print and cut out much more quickly.

Triangles arranged in rows. Each triangle is filled with one of seven patterns. There are white, yellow and magenta triangles.

My adventures in 3D printing: Seven Triples puzzle

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

There are seven kinds of shape. There are three copies of each shape. The pieces like to group together in threes.

Can you arrange the pieces into seven groups of three so that for each possible pair of shapes, there is one group containing that pair?

Try to do it without paying attention to colours first, then try to rearrange the pieces so each group has a piece of each colour in it.

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