A brief history of the Mathematics Learning Centre (1992 - )
By Geoff Coates
April 2001
(Updated August 2006)
The Mathematics Learning Centre was officially opened on 27 July 1992 by Professor Ian Falconer, Deputy Vice-Chancellor (Academic) but the wheels had been set in motion a year earlier when Liz Cousins (Applied Mathematics) and Alison Wolff (Pure Mathematics) applied to the National Priority Reserve Grant Scheme for funding to start a University-wide mathematics/statistics support service. Approval came in November 1991 and the doors opened in time for Semester 1 exams the following year.
In 2002 the Centre become the Mathematics Learning Service within the newly formed Learning and Teaching Development Unit (renamed and expanded in 2005 as the Centre for Learning and Professional Development). In September 2011 the name changed to the Maths Learning Centre.
The Maths drop-in service: This student service has been part of the MLC from the beginning and opened its doors on Monday 15 June 1992 (the last week of 1st Semester). There were six visits on the first day and there have been more than 26,500 since then. In 2000 the 'drop-in' service topped 2000 visits for the first time, even though the academic year was shortened by two weeks!
The Drop-In Room 1992-1998 (Hughes Plaza)
The "goldfish bowl" Drop-In Room 1998-2002 (Top floor Staff Club)
The Drop-In Room 2003- (Schulz Building)
Other Activities: Over the years the MLC has been involved in preparing and delivering many bridging courses, foundation courses and workshops. The service continues to develop hard copy and web-based resources and teaches a Level 1 course in Data Management abd Interpretation. In 1996 the MLC hosted the Australasian Bridging Mathematics Network conference. MLC staff are actively involved in the University community, particularly as members of Faculty Learning and Teaching committees.
Our Logo: The MLC logo is a pentagram (or five-pointed star) with "spikes'' half way along each point. The overall shape is reminiscent of an early stage of the Koch Snowflake fractal but doesn't exhibit self-similarity (ie. the spikes added to each side are not copies of the original pentagram).
Although the "spiky pentagram" was originally chosen for the MLC logo because "it looked the part", it belongs to a mathematical story which I think makes it a highly suitable symbol for the MLC.
The logo belongs to a set of six shapes, or prototiles, derived by English mathematician Roger Penrose in the early 1970's which, when used to tile the infinite plane, can only produce a pattern that never repeats itself in a rectangular sense (the way wallpaper patterns do, for instance). Such tilings are called "aperiodic".
(Note the use of four jigsaw-style "keys" to restrict the range of possible joins.)
How Penrose achieved this feat is an intriguing story. Click here for a more detailed description.
Other mathematicians had already produced six tile sets based on squares but the Penrose set, being based on pentagons, was capable of refinement to the point where only two tiles were needed. One pair is known as the "kite" and "dart" tiles:
(These tiles are only allowed to be be joined with corners of the same colour touching.)
At the time there were few obvious uses to which such theory could be put. The geometric properties of the shapes were interesting (for instance the ratio of long to short sides of the kites and darts is the Golden Ratio) and Penrose tilings are aesthetically pleasing when used for mozaics and quilts.
For example, here is a tiling based on an alternative tile pair (the "golden quadrilaterals"). The pattern does exhibit a kind of symmetry, known as "five-fold symmetry". Every rotation of 
about the centre is indistinguishable (like a pentagon):
© Copyright Roger Penrose.
In the early 1980's metallurgists encountered crystalline structures in certain alloys of aluminium which exhibited the supposedly physically impossible five-fold symmetry. As a result, the mathematics developed to study Penrose tiles has become invaluable in the field of what is now known as "Quasicrystals". (Indeed the mathematical framework is still under construction.)
Since the Mathematics Learning Centre helps students develop as mathematical thinkers, it seems appropriate to have as our logo a shape which appeared in the developmental stages of a rich, varied and applicable field of mathematics.
It is rare to see the steps towards the discovery of something as elegant and complete as these tile pairs. Often, especially in maths courses, we are presented with only the final result of a great deal of thinking by a great many people and presume that it popped fully formed into the brain of a single genius. While Roger Penrose is without doubt a genius, it's nice to know that his work took time to evolve.
Next time you are intimidated by a "clever mathematical trick" and think "I would never have have come up with that, I must be stupid", consider the MLC logo and remind yourself that you are not.
References and Further Reading
Math. Intelligencer, 2 (1979) pp. 32-37 [Roger Penrose describes how he did it.]
Tilings and Patterns, Grunbaum B, Shepard G, Freeman 1987 [Chapter 10 in particular. Note Kepler's figure Aa in the frontispiece.]
A discussion of Quasicrystals in alloys of aluminium by Ron Lipshitz. [Accessed 8/12/05]
A java applet to make your own Penrose tilings. [Accessed 8/12/05]
The Pacific Institute for the Mathematical Sciences Newsletter, Winter 2001, Vol 5 Issue 1 [Robert V. Moody discusses the development of aperiodic tiling as part of an address to Graduate students. Also available at the PIMS website http://www.pims.math.ca/publications/.]
