Back in November, I posted a collection of some of my favourite Desmos creations up to that point. Having made quite a lot of material since then, including some using different software and media, I thought it was about time to collate some of the highlights again…

After a colleague mentioned Dudeney’s dissection, I showed a 3D printed hinged version to some pupils, who seemed captivated by it. This inspired me to explore further. First up, I challenged myself to use Processing (in which I am relatively inexperienced) to create an animation showing a fluid transition between the two states:

I then got the idea that it might be possible to make a tiling pattern based on this dissection, and it was very satisfying to see this come to life in Desmos:

After this, I wondered if something similar might be possible with other dissections, and eventually I developed this sliding hexagon-square tiling:

Having seen an image of a tiling on a Poincaré disk, I started to play with this, but only really got as far as being able to draw any circular arc within the disk that meets the boundary at right angles:

A piece of geometric art by Regolo Bizzi inspired several of us on Twitter to experiment, and it was interesting to try to generalise it:

This trace and zoom version, based on the same idea, was quite challenging to work out:

Occasionally, others on Twitter have specifically asked for me to make something. This creation was the result of one such request:

This animation began as a straight attempt to copy something I had seen elsewhere, but it evolved as a result of a couple of ‘what if’ questions: What if it spins? What if there are multiple arms?

Having seen an intriguing animation shared on Twitter (original source unknown), I felt obliged to make my own version so I could play with the parameters and see what would happen:

The following came out of an exciting impromptu discovery during a lesson. I posed a question to the class about the number of ways to pick two teams from an even number of people. Their approach was completely different to mine, but entirely valid, and resulted in a conjecture that we subsequently proved. Here are the details, followed by a representation of the problem in a 3D print:

I went through a bit of a modular origami phase (warning: it was quite addictive!):

With Desmos, I found a way to shade alternate regions bounded by a set of curves:

Just before Christmas, Taylor Belcher shared a static image of a dabbing snowman in Desmos. It was practically begging to be animated!

@3Blue1Brown shared a brilliant video showing how it is possible to solve the Towers of Hanoi by counting in base 3. This meant it should be possible to programme a solution, so I gave it a go:

After a recommendation from Roy Wiggins, I played with some software called Fragmentarium, which is great for making high-definition images of regions defined by inequalities:

@konkretegifs is very new to Twitter. His style of hand-drawn mathematical art animations has already inspired many others to have a go, including me:

Most recently, I have been collaborating with Annie Perkins about 2D representations of 3D polyhedra. She has been doing some explorations on paper, constructing diagrams using compasses and a ruler, whereas I have adapted some of her ideas to make animations in both Desmos and Geogebra: