The Hexastix sculpture has been on my to-do list since I first saw it on Twitter over a year ago. And yesterday I made one! And, well, the construction of this slightly bonkers mathematical structure made from 72 pencils, first created by George W. Hart, was so immensely satisfying that I've been inspired to blog to encourage EVERYONE to make their own!
Now life's too short to make your own set of instructions when there are perfectly good instructions already out there, so I'll just share a few tips that I learnt from making some rookie errors on my first attempt, and then link to the excellent instructions that I used.
But before I begin, here's my finished Hexastix! I think I'd describe it as a 3D structure made from four intersecting hexagonal 'prisms'...
Basically, you need 72 hexagonal-cross-sectioned pencils (with maybe a few spares) and a pack of elastic bands. You could use wooden skewers or toothpicks instead of pencils, but you'd miss out on the ultra-pleasing hexagon-shaped holes that emerge when using the pencils. I chose to use these plain wooden pencils and uncoloured elastic bands, as I wanted a 'natural' look, but TIP 1 is that colour is a BIG HELP when constructing this sculpture, so you may choose to use four different colours of pencil, or four different colours of elastic band. I resorted to taping a strip of coloured paper around one pencil in each of the four sets (below right) to help with the construction process, after getting in a complete muddle on my first attempt!
And TIP 2: unsharpened pencils are a wise choice if you don't fancy stabbing yourself several times in the construction process!
I would advise first watching this entertaining video by Matt Parker (@Standupmaths), so that you have an overview of what it is you'll be doing before you actually get started on the building process.
For the actual Hexastix construction, however, I recommend the same set of photo instructions that Matt does, these by Alejandro Erickson.
TIP 3: after my false start, I labelled my pencils in the same colours as Alejandro uses, and then started by orienting my structure to line up with his photos each time, so that I could follow his instructions exactly. However, soon enough, as the little hexagonal gaps start emerging, you'll get the hang of the construction and will just go for it! Once you have your initial 'Level 1' set of 4 hexagonal prisms, you 'expand' them twice more to achieve your very own Level 3 Hexastix!
TIP 4: be aware that the elastic bands will deteriorate over time. To preserve them as long as possible, keep your Hexastix out of direct sunlight.
A highly recommended mathematical build - enjoy!
Colouring books. They're everywhere. They've taken over bookshops across the world, and colouring pencils can't be made fast enough to meet demand. But what do they have to offer students and maths lovers?
At my previous school, after re-discovering colouring books myself one lazy summer, I started a colouring club. I purchased a couple of animal-themed colouring books (everybody likes animals) with a focus on images that employed repeating pattern and/or symmetry, as I wanted to include a maths theme. I also found a great 'Ultimate Dot-to-Dot' book. I cut the pages out and kept them in a folder, in plastic pockets, and simply photocopied the designs as and when the students selected them. That way I kept the originals as 'masters'.
I have to confess that initially I rather stereotypically imagined that it would be a club that only appealed to girls, but the reality surprised me - the majority of the 12 or so regular attendees were boys from Years 7 and 8, many of whom also coloured at home. And it was boys that told me "This is the best club ever! Can you run it every lunchtime?!" They were in charge of getting out the coloured pencils and the folder of colouring sheets, and then they sat down, coloured in, and chatted happily all lunchbreak. So, it was an absolute success, and apart from a little organisation at the start of the year, took no planning at all on my part (result!). If you would like to start your own colouring club you are welcome to use this editable poster to advertise it (click on the middle image for the file; you will need to download the free font 'Back To School').
Mathematical colouring books
But what if you like your colouring even more mathematical? Well, there are several beautiful, maths-themed colouring books out there, as well as several free resources which I will detail in the next section. Perhaps the most well-known of these books is Snowflake Seashell Star (below, entitled 'Patterns of the Universe' in the US) by Alex Bellos and Edmund Harris. It's a lovely book, chock full of beautiful mathematical patterns, and is divided into two sections: a section of images to colour in, and a set of instructions and templates allowing you to create other patterns, such as an Ulam spiral and a hyperbola, yourself. There is also an index with further information on each type of pattern. This makes it informative as well as recreational; one to treasure.
Free mathematical colouring resources
However, there really isn't any need to spend money on mathematical colouring books if you don't want to; some very generous and creative souls have shared beautiful mathematical images for you to download, print and colour for free.
The first of these is a beautiful downloadable colouring book by Marshall Hampton, aptly named A Mathematical Colouring Book. It is a really high quality text, full of elegant mathematical curves and patterns (see below), with a short description of each figure at the end of the book. A great addition to any colouring collection!
When I left my first teaching school (the one I’m back working at again now) I decided to make a piece of art as a leaving gift for my colleagues in the maths team. I’d seen an image on Pinterest of a mural made from different coloured paper tetrahedra, and wanted to try it for myself. However, being a maths teacher, I was intrigued by the possibilities of tessellating smaller tetrahedra within the gaps left by bigger tetrahedra....
Now I know that A-sized paper has some pretty cool properties, so, using the photocopier I reduced an A4 tetrahedron net down through the various A-sizes - and, yes, I made some lovely discoveries (which made perfect sense once I started thinking about it)!
Each iteration of A-sized paper decreases in area by half, (so the side lengths decrease by a factor of 1/(sqrt2)): A5 is half the area of A4, A6 half the area of A5, and so on. So the base of an A6 tetrahedron is a quarter the area of an A4 base, meaning that four A6 tetrahedron bases can be packaged in the gap left by an A4 tetrahedron. I played around and found some other combinations (see some examples below).
I printed and cut out all my nets, assembled my different sized tetrahedra (step-by-step instructions to follow below) and played around with lots of different arrangements. When finally happy, I stuck them down onto a ready-made canvas.
A week ago my ex-colleague Ali got in touch because she wanted to try the activity with her class. I talked her through the instructions and her students went on to produce the wonderful artwork below :)
Here are the step-by-step instructions if you would like to try this activity with your students.
I teach maths. I'm a bit arty. I like to combine the two.