Mathematical Art & Play
We believe maths is something that can provide a source of enjoyment, a way for people to express themselves, and a way to bring people together.
So we engage in mathematical art and play activities. To find out more about any of these activities, please contact us.
One Hundred Factorial is a gathering of staff, students and friends to solve puzzles and play mathematical games together.
We have face-to-face games and puzzle sessions regularly. You can also follow our puzzle-solving on social media.
Everyone is welcome to One Hundred Factorial, you don't have to be associated with the University of Adelaide to join in. Children are welcome, but for legal reasons you must stay at the event with your children - we cannot be responsible for supervising them.
There is a weekly face-to-face puzzle and games session during Semester 1 and 2 teaching weeks. These are the current details of the face-to-face sessions:
Days: Fridays, beginning on 6th August 2021
Time: 12noon to 2pm.
Place: Level 3 East Hub Central, just outside the Maths Learning Centre (on special occasions it may be in another location).
We have some ground rules about how we interact with each other to make sure it stays welcoming. At One Hundred Factorial it is always ok to:
- grab a pencil/marker and start writing,
- say you don't understand,
- ask someone to explain their thinking,
- try out half-formed thinking',
- just watch,
- hive off to have a go on your own,
- leave one puzzle and go to look at another one,
- ask someone to say what's happened so far,
- express delight loudly,
- draw pictures, make a model, be the model,
- say you still don't understand,
- stop and make a new notation,
- try a different way,
- move the conversation in a new direction,
- investigate something else related,
- Our lecturer David occasionally writes about the puzzles we do at One Hundred Factorial on his blog.
- This blog post describes the history of the One Hundred Factorial sessions.
- David gave a seminar on One Hundred Factorial: Playful and Joyful Maths at the MASA Annual Conference in April 2017.
- Join in with the conversation on Twitter by using the hashtag #100factorial.
Our lecturer David Butler creates mathematical artworks, usually of a collaborative constructive nature.
Space-filling / mind-filling
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.
Special thanks go to Nicholas Crouch, Daniel Kon and Carolyn Haese for effort in construction.
My Piece of Pi
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.
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.
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.
Construction of the Stage 6 model in 2011
MLC lecturer David K Butler likes to create and collect puzzles and games.
Here are some that you might find interesting:
|Favourite One Hundred Factorial puzzles||A collection of eight favourite puzzles that have been used at One Hundred Factorial|
|Puzzles created by David K Butler||A collection of puzzles created by David K Butler|
|Logic puzzles that are fun to do collaboratively||
These logic puzzles are used at One Hundred Factorial for group problem-solving:
|16 Sudokus||A set of 16 sudoku puzzles with a connection|
|Quarter the Cross||An open-ended puzzle with a creative flair (Twitter: #QuarterTheCross)|
|4-Dimensional Noughts and Crosses||a two-player game that requires spatial thinking in four dimensions|
|Which Number Where||A two-player game that is a bit like battleships and a bit like Guess Who, and involves careful logical deduction.|
|Digit Disguises||A two-player game of algebraic deduction, that is a little bit like battleships and a little like Cluedo.|
|Number neighbourhoods||A two-player game of analytic deduction, that is a little bit like battleships and a little like Cluedo.|
|Giant SET||Cards for the game SET that can be printed on A4 paper to make giant cards. (SET originally designed by Marsha Falco and published by SET enterprises)|
|Bodyscale Prime Climb||A version of the game Prime Climb that can be played with humans as the playing pieces. (Prime Climb originally designed by Dan Finkel and published by Math4Love.) The cards can also be printed 32 to a page to create a deck of small cards that you can arrange on a table. Download the cards and spinner template, and a version of the rules.|
|Extended Prime Climb cards||A version of the Prime Climb cards (based on the board game originally designed by Dan Finkel and published by Math4Love) that goes from 1 to 144 with an extra colour for eleven. These can be printed 32 to a page to make an extended deck of cards to arrange on a table.|
|Jenga Views||Twenty puzzles of increasing complexity where you need to build a structure from Jenga blocks to match the three views (orthographic projections) given.
If you want to make your own, the template is in this SVG file (which you can edit with Inkscape). (The original version of this was made by JD Hamkins using differently-sized blocks, and I have redrawn it to use Jenga blocks.)
Occasionally, MLC lecturer David K Butler gives seminars on maths or maths-related topics, where the focus is on the fun or interest of the maths. Find out more about the past seminars here.
Playful and joyful maths (keynote at MAVCON 2017)
This keynote presentation was given by David Butler at the MAV Annual Conference in Decemeber 2017.
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.
To view the prezi from the seminar on Prezi.com, follow this link: Playful and Joyful Maths MAV Keynote on Prezi.com
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
One hundred factorial: playful and joyful maths
This workshop was given by David Butler at the MASA Annual Conference in April 2017, and also at TMC 17 in July 2017.
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.
To view the prezi from the seminar on Prezi.com, follow this link: One Hundred Factorial: Playful and Joyful Maths on Prezi.com
The Queen of Hearts plays noughts and crosses
This workshop was given by David Butler at the MASA Annual Conference in April 2017.
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.
My favourite formula: ⌊ n!/e ⌉
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.
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.
To view the prezi from the seminar on Prezi.com, follow this link: n factorial on e on Prezi.com
Eigenvalue magic tricks
This seminar was given by David Butler as part of the School of Mathematical Sciences Undergraduate Seminar Series in August 2013.
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.
To view the prezi from the seminar on Prezi.com, follow this link: Eigenvalue Magic Tricks on Prezi.com
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
Secrets of Alice in Wonderland
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.
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.
To view the prezi from the seminar on Prezi.com, follow this link: Secrets of Alice in Wonderland on Prezi.com
To view the video of the seminar on YouTube, follow this link: Secrets of Alice in Wonderland on YouTube