Mathematical Art & Play

My Piece of Pi (MLC 32nd Anniversary edition)

On 22nd of July 2024, in celebration of the shared human activity that is maths, and also the 32nd Anniversary of the Maths Learning Centre, the digits of π will be turned into an art installation at the University of Adelaide.

 You are invited to decorate your own piece of π for the artwork.

 The rules:

• The page must be A4 white paper, with a 1.5cm border of blank space left all around the edge.
• Draw one digit taking up the whole page.
• The shape of an ordinary hindu-arabic digit (0,1,2,3,4,5,6,7,8,9) must be clearly visible.
• You are encouraged also write a birthday message to the MLC or a memory of the MLC on the back.
• Either deliver in person, post, or scan and email to the MLC by 20th July 2024

Space-filling / mind-filling is an artwork designed by David K Butler, with students and staff of the University of Adelaide assisting in its construction. Its construction began in 2016 and has continued since then. It is currently located on Level 3 of  the Barr-Smith South building at the University of Adelaide, just outside the Polygon Lecture Theatre.

The artwork is built from shapes called Silver Rhombic Dodecahedra, which have been made from origami units folded from A4 paper according to a design by American origamist Nick Robinson. 

PDF: POSTER AND FOLDING INSTRUCTIONS

VIDEO: Folding Rick Robinson's rhombic unit

Special thanks go to Nicholas Crouch, Daniel Kon and Carolyn Haese for effort in construction.

A mathematical artwork designed by David K Butler & drawn by you.

On International Pi Approximation Day (22nd of July) from 2012 to 2018 we encouraged people to help draw and decorate more than 1000 digits of the decimal expansion of the number pi in chalk on the North Terrace footpath and the University of Adelaide grounds. This artwork is called My Piece of Pi.

2012 version

Artist statement

This artwork speaks about the wonder of maths as a world of its own and the wonder of maths as a human endeavour.

The number π is part of the very fabric of the universe: it is there in every circle, and appears in the mathematical descriptions of many seemingly unrelated things. Yet it is impossible to write down exactly as a number. It cannot be written as a fraction, and its decimal expansion continues forever with no comprehensible pattern. This artwork highlights this paradox: a number so very fundamental that is so very unknowable. The digits will be written on the ground where people often walk emphasising the pervasive fundamental nature of π. But the day chosen to create the artwork is Pi Approximation Day, emphasising that however many digits we draw it is still only an approximation.

On the other hand, even though π is a fundamental universal constant, it is still a human construction. Humans had the idea of π and thousands of years of human ingenuity have gone into understanding the number. Indeed, we are only able to know as many digits of π as we do because of complex mathematical theories developed in the last century. Members of the community will be engaged to help draw the numbers, to emphasise the human element to mathematics. Each participant will choose their own style, colour and decoration and the total effect will highlight that our knowledge of π is the creative work of hundreds of people over time.

Finally, the collaborative nature of the artwork has further meaning: mathematics and art are not just reserved for so-called 'mathematicians' and 'artists'. In fact, these pursuits are part of being human and any person can engage in them. Observers of this artwork do not have to be merely observers. Instead, they can participate in this mathematical artistic expression, and then stand over one of the digits and claim: here is My Piece of Pi.

Used public transport tickets were attached to wooden boards according to simple rules in order to create a randomly-generated cellular automaton.

View photos of the construction.

Artist statement

This artwork is about the fundamental struggle in mathematics between randomness and determinism and between simplicity and complexity.

Public transport tickets of the same shape were added to each panel according to four simple rules, but the choice of where to place them was left up to the people who participated. This interplay between simple rules and random behaviour has resulted in complex maze-like structures, each of which is different and yet somehow similar - each is different because of the randomness, but each contains similar structures because of the common set of rules. Moreover, while the tickets appear to be the same shape, the slight random imperfections in their shape have caused unexpected perturbations in the regular pattern produced.

When looking at the artwork, viewers are encouraged to look past the randomness to discover the rules used to construct it, and to notice the common structures in the maze that were created as the tickets were added. Thus the viewers participate in the fundamental tasks of the mathematician - to discover simplicity behind complexity, and to find the deterministic beneath the random.

The Sierpinski Sponge is a fractal that lives in 3D space. It is like a triangular pyramid, but it is made out of smaller pyramids, which themselves are made out of smaller pyramids, which themselves are made out of even smaller pyramids, and so on forever.

In 2011 and 2014, we built models of the Sierpinski Sponge out of paper and sticky-tape. Four small pyramids were joined at the corners to make a Stage 1 model. Then four Stage 1 models were joined to make a Stage 2 model. Then four Stage 2 models were joined to make a Stage 3 model, and so on.

You can see Stage 0, 1, 2, 3 and 4 hanging in the ceiling of the MLC Drop-In Room near the entrance.

Construction of the Stage 6 model in 2011

• Pyramid construction day 2011
• Stage 6 Sierpinski Sponge Construction Day 2011
• Stage 7 Sierpinski Sponge Construction Day 2014

Maths Sheep Play Sheep is a picture book that MLC lecturer David Butler wrote and illustrated in August 2023 in honour of Children's Book Week. It is inspired by Where is the Green Sheep? by Mem Fox and Judy Horacek.

You can download a PDF of the book, or watch David read the book aloud on YouTube.

This keynote presentation was given by David Butler at the MAV Annual Conference in Decemeber 2017.

Abstract

I love maths. I derive great joy in finding the maths around me, talking about it, and solving problems I've never seen before. Yet I know not everyone experiences this kind of mathematical joy. Some find the concept of joy in maths a little alien. Some like maths but struggle to find joy in the maths they face daily. Some do have the joy but wonder how to help their friends, students and colleagues find it. I have come to realise that my own joy in maths has been created by a continual and concerted effort to play. I've organised more time to play with maths in my life, but also infused a playful attitude into the daily maths I do with students.

This session is about how to take a playful approach to your maths in order to find more joy. I'll talk about what both joy and play feel like and how they make a difference to growth mindset. I’ll share my experiences running puzzle sessions and in providing maths learning support to thousands of students. You will get a chance to engage in some playful maths activities, and to find the play in maths that at first looks like hard work or like the 'same old thing'. I hope that you will learn some strategies to be more playful and hence find more mathematical joy.

Prezi

To view the prezi from the seminar on Prezi.com, follow this link: Playful and Joyful Maths MAV Keynote on Prezi.com

Further Resources

I (David) mentioned several puzzles and other resources in the presentation, and here are links to most of them. Note that you can find information about One Hundred Factrorial and about my mathematical art projects here on this webpage by clicking on the tabs. (Those puzzles that I don't have links for, feel free to just take the pictures from the presentation.)

• My blog post about the Zero Zeros problem
• My blog post about the Spotless Dice problem
• My blog post about the bodyscale Prime Climb game
• My blog post about the Panda Squares puzzle
• Sara Van Der Werf's blog post about Play Tables in High School maths classrooms
• Link to the Math in Your Feet website -- Malke Rosenfeld's work on whole-body maths learning
• My blog post about the frustrated cone
• My blog post about 65536
• Link to information about the Notice and Wonder routine
• Link to the Open Middle problems website
• Link to a #MTBoS twitter search

This workshop was given by David Butler at the MASA Annual Conference in April 2017, and also at TMC 17 in July 2017.

Abstract

In this session, we'll explore what it means and what it feels like to engage in joyful play in maths, and how to encourage the atmosphere that allows for it. I'll describe what I have learned at the puzzle and games group "One Hundred Factorial" over the last ten years, and give participants a chance to experience a bit of what I do there for themselves. Come prepared to play with some puzzles together.

Prezi

To view the prezi from the seminar on Prezi.com, follow this link: One Hundred Factorial: Playful and Joyful Maths on Prezi.com

This workshop was given by David Butler at the MASA Annual Conference in April 2017.

Abstract

In this session, we'll explore the fascinating world of finite geometry through the medium of noughts and crosses and a deck of cards. The ideas here would be useful for extension of students at many different year levels and levels of maths skill.

Resources

• PDF version of the handout, which has templates for the three types of noughts and crosses games: Original, Affine and Projective.
• Picture of the special dealing of cards in wide format and tall format.
• PDF version of the poster covering the same ideas as the seminar.

This seminar was be given by David Butler as part of the School of Mathematical Sciences Undergraduate Seminar Series in September 2014, and also again at the MASA conference in 2018.

Abstract

What is this formula? Why does it use those strangely mismatched brackets, and why does it use both factorial and the number e? What is it supposed to calculate? And why would someone love it so much that they put it on a t-shirt? In this seminar you will find out the answers to all of these questions, and also find out what derangements have to do with Taylor's theorem.

Prezi

To view the prezi from the seminar on Prezi.com, follow this link: n factorial on e on Prezi.com

This seminar was given by David Butler as part of the School of Mathematical Sciences Undergraduate Seminar Series in August 2013.

Abstract

Eigenvalues are awesome, but students rarely get the chance to see just how supremely awesome they are. In this talk I’ll tell you some awesome truths about eigenvalues that you don’t get to see in first year, and show you their proofs, which happen to contain some of the most clever magic tricks in the whole of maths.

Prezi

To view the prezi from the seminar on Prezi.com, follow this link: Eigenvalue Magic Tricks on Prezi.com

Handout

To download a pdf version of the handout, which contains more cool eigenvalue proofs than in the seminar, follow this link: Eigenvalue Information and Proofs handout

This live streaming show was presented by David Butler and Cobi Smith at the Royal Institution of Australia as part of Science Week 2012 and the Great Big Science Read project. 

Abstract

Lewis Carroll's Alice in Wonderland is famous as a story that doesn't make much sense -- unless you know that the author was a mathematician. This part-performance, part-discussion introduces you to chapters of Alice in Wonderland with mathematical links. Mathematics is an evolving field of ideas now, as it was when Alice in Wonderland was written in the 19th century.

Prezi

To view the prezi from the seminar on Prezi.com, follow this link: Secrets of Alice in Wonderland on Prezi.com

Video

To view the video of the seminar on YouTube, follow this link: Secrets of Alice in Wonderland on YouTube