A conversation about mathematics and education inspired by a hundred square. Presented by Katie Steckles and Peter Rowlett, with special guest Susan Okereke.

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

This is something I’ve wanted to make for a long time: a literal sieve of Eratosthenes.

This is a collection of trays which stack on top of each other.

Each tray has a grid of holes, with some holes filled in. The tray with a “2” on it has every second hole filled in; the tray with a “3” has every third hole filled in; and so on.

When the trays are stacked together, the holes you can see through correspond to prime numbers: every other number is filled in on one of the trays.

I went through quite a few iterations of this design. The first version was a series of nesting trays. After printing it, I realised that you might want to put the trays in a different order. After that, I did a lot of fiddling with different ways of making the plates stack on top of each other. The final version has sticky-outy pegs at each corner, and corresponding holes on the other side. I had to add a fair bit of margin around the holes so the wall didn’t go wiggly when printed.

In this series of posts, Katie investigates simple mathematical concepts using the Google Sheets spreadsheet app on her phone. If you have a simple maths trick, pattern or concept you’d like to see illustrated in this series, please get in touch.

Having spoken at the MathsJam annual conference in November 2016 about my previous phone spreadsheet on multiples of nine, I was contacted by a member of the audience with another interesting number fact they’d used a phone spreadsheet to investigate: my use of =MID() to pick out individual digits had inspired them, and I thought I’d share it here in another of these columns (LOL spreadsheet jokes).

It quite quickly went viral, or as relatively viral as a maths game can get, with people tweeting their high scores and posting the link to reddit and Hacker News. I realised fairly soon that I should put in some stats tracking, to see if there were any interesting patterns in the data (and also to inflate my ego as the “games played” counter went up). I missed the first big spike in traffic, but on the 9th of March I wrote a script which saved a record of each game to a database.

The mad rush settled down quite quickly but there were still occasional spikes as different sites or people with lots of twitter followers found the game. Now, after two months, I’ve got data for just under 350,000 games. That’s a decent amount of information!

There’s been a lot of maths news this month, but we’ve all been too busy to keep up with it. So, in case you missed anything, here’s a summary of the biggest stories this month. We’ve got two new facts about primes, the best way of packing spheres in lots of dimensions, and the ongoing debate about the place of maths in society, as well as the place of society in maths.

A surprisingly simple pattern in the primes

Kannan Soundararajan and Robert Lemke Oliver have noticed that the last digits of adjacent prime numbers aren’t uniformly distributed – if one prime ends in a 1, for example, the next prime number is less likely to end in a 1 than another odd digit. Top maths journos Evelyn Lamb and Erica Klarreich have both written very accessible pieces about this, in the Nature blog and Quanta magazine, respectively.

This year, I’ve been thinking about prime numbers, and my hosting provider has run another sale on domain names. So, I’ve bought isthisprime.com. You can probably guess what I’ve made it do.