## You're reading: Posts By Andrew Stacey

### Doughnuts in the Sand

This is a guest post by semi-regular guest author, mathematician-turned-maths-teacher Andrew Stacey.

I like having something mathematical to think about for times when I’m, for example, waiting in a queue to get into the supermarket. Annie Perkin’s Math Art Challenge has been a good source of such of late. These are a series of mathematically-inspired artistic activities, ranging from designing celtic knots to constructing origami polyhedra and everything in between.

My eye was caught by one on sandpiles – I’ll explain exactly what they are in a moment. One feature that made it attractive was that it was quite simple to write a program to generate diagrams. I find that the maths that interests me usually comes from looking at variations, and for that I need to generate a lot of examples. Doing them by hand quickly becomes laborious. So I whipped up a program (which I later converted to an online version) and ran it a few times to see what happened.

### Fi-Bee-onacci

Andrew Stacey: I have a confession to make that would probably get me thrown out of every respectable Mathematics Society – were I to belong to one.

I am not a fan of the Fibonacci sequence.

Neither am I keen on the golden ratio. It’s not even transcendental.

It’s not really their fault, it’s just that they get levered in everywhere whether they belong there or not. Particularly in discussions of nature and beauty, and this is exemplified by that ridiculous origin story. We’ve been subjected to a variety of bizarre origin stories over the years (cough radioactive spider cough) but the rabbit story is another level of bizarre.

So I was intrigued, and then delighted, when one of my students, who is a bee enthusiast, told me about a genuinely natural occurrence of the Fibonacci sequence in the ancestry of bees.

I’ll let her take up the story.

### That which we call an identity

I’m grateful to Jemma Sherwood and Rob Low for reading an early draft of this and for their comments thereon. All opinions are, of course, my own.

This post is inspired by something that I see crop up now and again in discussions with other Maths teachers. It usually manifests itself as a rallying cry to use ≡ in place of = in identities and reserve = for equations. My standard response is to mutter something about identities being equations and leave it at that. But in the latest round, Jemma Sherwood challenged me, in the nicest possible way, to explain a bit further. This is that explanation.

Although I’m going to state my case here, I’m well aware that there are different opinions. In matters of opinion, such as this, agreement and disagreement is less important than that all sides think. So if what I write seems to you wrong, that’s fine so long as it makes you think about why you think that it is wrong.

### Tessellating Tricurves

Tricurves were introduced to the Aperiodical audience via Tim Lexen‘s posts Bending the Law of Sines, Combining Tricurves, Phantom Tiling, and (joint with Katie Steckles) Making Tricurves. Like Tim and Katie in that last post, when introduced to a new concept I like to play around with it to see it from different perspectives. Tiling is a topic in maths that is near enough to my speciality that I feel I should be able to understand it, but far enough that I don’t feel any pressure to be an expert – perfect conditions for playing with the concepts.