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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.

My adventures in 3D printing: Prime number sieve

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

Hand holding a stack of 3D printed squares, with holes cut out.

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.

Four trays, corresponding to numbers 2,3,4 and 5

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.

You can download .scad and .stl files for the prime number sieve at Thingiverse.

My adventures in 3D printing: Golomb ruler

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

At the start of the Summer we (I) bought a new 3D printer for the department, a FlashForge Dreamer. It’s got two extruder heads, so it can do two-colour prints.

To test that out, I designed this Golomb ruler. It’s a straightedge with marks at 0, 1, 4 and 6 cm. The idea is that you can measure 1, 2, 3, 4, 5 or 6 cm by lining up against different pairs of marks. I recently did a silly Twitter thread on this subject.

As you can see from the photo, two-colour printing isn’t quite as straightforwared as it could be. Because both nozzles need to stay hot, while one colour was printing the other just oozed out and made a mess. There are some settings on the printer you can change to try to reduce this, but I haven’t got the hang of it yet.

You can download .scad and .stl files for the Golomb ruler at Thingiverse.

My adventures in 3D printing: Wallis’ Sheldonian theatre roof

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

Several dozen black beams woven together to make a single structure, supported only at the edges.

The roof of the Sheldonian theatre in Oxford, built from 1664 to 1669, is constructed from timber beams which are unsupported apart from at the walls, and held together only by gravity.

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