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Mandala May-hem!

21/5/2020

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This month, Lindsey Bowkett (@MissBowkett) and I have been challenging ourselves to draw a mandala a day in May. We both wanted to get back into the swing of making art regularly, and when Lindsey coined the hashtag #Maydala, we were off!

We have been delighted to have been joined on the journey by many other maths teachers across Twitter – here are some of their wonderful designs. For even more marvellous mandala mayhem, do check out the #Maydala hashtag!
@giftedHKO
@KierstyT
@giftedHKO
@MathsJanet
@CarolineDimelow
@japleen_kaur1's daughter
@b_karadia
@fractionfanatic
@hillaust
@b_karadia
@MissBowkett
@japleen_kaur1
@PaulaKrieg
@hillaust
@987jude
@MathsJanet
Mandalas are rich in mathematics (circle geometry, reflective and rotational symmetry), and provide useful practice with geometry tools including rulers, compasses and protractors. Several teachers have asked how to introduce the activity to their students, so I have decided to collate the ideas and resources from my original twitter thread here.
The word ‘mandala’ means ‘circle’ in Sanskrit, and mandalas have a deep spiritual or cosmic meaning in many cultures and traditions. For our #Maydala purposes, a mandala is any circular design exhibiting pattern and symmetry.
Mandala making is accessible to all. The repetitive nature of these designs means that drawing them can be a wonderfully absorbing and meditative process, and it's a process that results in stunning geometrical patterns - bonus!
Designs can be drawn entirely freehand, or using a mixture of freehand and compass/ruler construction, or solely compass and ruler construction. Anything goes! Some participants are even using technology or origami to make their mandalas, with stunning results:
@RobRubix
@PaulaKrieg
@rrmmff
So, how do you get started? These Wikihow instructions are really clear and easy to follow:
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And this set of video tutorials from Kathryn Costa (@100mandalas) are very useful too.
Lindsey (@MissBowkett) has made a series of lovely timelapse videos showing her process, such as this one:

My first ever time lapse video ... #Maydala @c0mplexnumber #Mandala #MandalaArt #Mindfulness pic.twitter.com/nkyqhPD4Mp

— Miss Bowkett (@MissBowkett) May 14, 2020
And Miss Konstantine (@giftedHKO) made this set of instructions for a fabulous cube mandala, which Becky Warren (@becky_k_warren) followed to make her version, coloured in with colouring pencils, below.
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But there are lots of other things you can do too!
How about making a mandala from objects around the house, or from things found on a walk outside? The artist James Brunt (@RFJamesUK) makes fabulous designs from found objects, or from the contents of his junk drawer!

Lockdown series pic.twitter.com/IR7CjB78dm

— james brunt artist (@RFJamesUK) May 17, 2020

Isolation April pic.twitter.com/5tSFrIz861

— james brunt artist (@RFJamesUK) April 26, 2020
Or if you have a pebble collection you could get creative and add some dotty colour. Check out this totally scrumptious work by the artist Elspeth McLean!
If you’ve got a Spirograph set gathering dust in a cupboard somewhere then this is the perfect excuse to dust it off and get spiralling. Metallic pens add that extra bling!
@c0mplexnumber
@PaulaKrieg
@c0mplexnumber
Fancy giving your compasses a workout? Islamic geometric patterns begin with a single circle, and are some of the most beautifully proportioned patterns in the world. Check out Samira Mian's (@samira_mian) Youtube channel for some clear and easy-to-follow tutorials. Here is a lovely circular pattern perfect for a mandala!
So, a plethora of resources and ideas to help you get started! If you post your finished artwork on Twitter, be sure to use the #Maydala hashtag. You can use it any time of the year - why not?!
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Mathematical Colouring Pages

2/8/2018

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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').
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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.
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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.
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Altair design
Altair design
Altair design
Altair design

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!
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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! :)
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    I teach maths.  I'm a bit arty.   I like to combine the two.

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