Mathematical Colouring Pages

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?

Colouring club

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.

Another good colouring book is The Golden Ratio Colouring Book, by Steve Richards (above left, and right). This consists of a series of decorative designs based around patterns formed from the Golden Ratio and Fibonacci Spiral, as well as other mathematical patterns such as the Vesica Piscis, the Flower of Life and the Koch snowflake.

And we mustn't forget the wonderful Altair Design books that many of us will remember from childhood. These have been updated to include patterns based on Islamic geometry, Penrose tiling and sets of colourable postcards. The images below were coloured by my mum, Judith.

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!

Martin Holtham (@GHSMaths) has used his amazing Desmos skills to create a set of stunning colourable images which he has shared on his Mathemart blog here. I particularly like his 'curve of pursuit', left. If you would like to learn how to draw these beautiful spirals yourself there is a set of instructions on my Mathematical art lessons page.

Finally, the talented Devan Matthews (@devan_matthews), a mathematical artist who works with Microsoft Excel, has shared some of his delicate images online for people to colour. He has also created an intriguing set of dot-to-dot maths art pictures.

Here are the links to Devan's sets of images:

• Mathematical art join-the-dots pictures
• Math art series 1 (three fold symmetry)
• Math art series 2 (four fold symmetry)
• Math art series 3 (five fold symmetry)
• More of Devan's blog posts with delicious geometrical curves and mandalas for colouring.
  

Examples of Devan's work are right and below.

I hope you find as much enjoyment in this beautiful selection of mathematical images as I have.

Happy colouring! :)