## Shape optimization

I found this board at the International Centre for Mathematical Sciences (ICMS) during a conference about shape optimisation and shape geometry. Talking to some of the delegates there I found out that the field is all about finding the best shapes to suit a purpose, and these purposes might come from physics, engineering, architecture, or simply pure mathematics. For example, the Reuleaux triangle is a shape of constant width (it has the same diameter wherever you measure it) but has an area 12% less than a circle of the same diameter. This makes it more efficient for making coins (our 50p piece is a similar shape but with 7 sides), manhole covers and even buildings.

I asked conference delegate Jimmy Lamboley what his favourite shape was, and he laughed and said “Anything but a sphere!”. He explained: ” The sphere is so often the answer to minimisation problems that I love to find the problems where it isn’t the case.”

The Reuleaux triangle is a great example of a shape more efficient than a circle. What’s amazing is that the corresponding question for 3D shapes (which shape of constant width has minimum volume?) is a problem still waiting for a solution.

## Fractal decorations

I found this blackboard in the maths common room of Lafayette College, a beautiful old campus university near the small town of Easton (just north of Philadelphia in the US). While the board contains some nice mathematics, I was particularly taken by the psychedelic fractal border on top of the board. I believe this was created by Professor Cliff Reiter, who has done a lot of research into visualisation and fractals, and who has an interesting textbook on the subject.

## Doors Open Day

On Saturday 28 September 2013 many interesting buildings in Edinburgh opened their doors to the public for Doors Open Day. One of these was ICMS – the International Centre for Mathematical Sciences – on South College Street. ICMS are in a building that used to be a church and still has a beautiful stained glass window, but now the only worshipping which goes on is for mathematics! Visitors were invited to solve puzzles and play mathematical games, and to draw their favourite maths on this blackboard. What would you have drawn?

## Christmas party song requests

On coming back to the School of Mathematics in Edinburgh in the New Year, I was amused by the blackboard in the common room. Christmas party songs had been written on the board during our end-of-year party, but in January, rather than rubbing them off to make space for mathematics, people had just decided to write their maths in the gaps between words. One of our postgraduates, Hari Sriskantha, noted that mathematics is like a weed that grows in unwanted parts of blackboards.

Do you have examples of this happening on your public blackboards too? If so, send them in!

## Sufficient criterion for pulling

This is the whiteboard of my officemate Alexandra Tzella, a postdoc at the University of Edinburgh working on fluid dynamics with Professor Jacques Vanneste. I liked the board for many reasons: the different colours that appeared after each new conversation, the lovely combination of algebra, analysis and ad-hoc diagrams, and of course the brilliant and rather racy title. Sadly Alexandra and Jacques were not investigating criteria for attracting the opposite sex in bars, but the criteria for determining the speed of a moving front (such as a fire spreading). It turns out that if the equation at the top is satisfied, then the speed of the front is determined by the behaviour of the fluid around a particular unstable fixed point.

[The part of the board spilling out on the left is mine – some residual calculations from the last Edinburgh MathsJam!]

## The Warwick maths train

This photo was sent in by Nicholas Jackson at the University of Warwick. He says that some years ago, when the Warwick Mathematics Institute was still up on the Gibbet Hill campus, before it moved into the new building down on main campus, an industrious graduate student drew a large picture of a train on one of the many blackboards dotted around the department. It stayed there for a good few years, until a well-meaning cleaner wiped it away. Fortunately, the original artist came back for a conference a few weeks later and redrew it while he was there. The train lasted for another few years until another well-meaning cleaner erased it. Nicholas took this photograph during his MSc sometime in 1996 or 1997 and thinks that the train finally disappeared in 1999 or 2000. Were you in Warwick at that time? Do you remember it? Do you have similar stories of surprising artwork appearing on boards in your department? Let me know!

## Mathematical palimpsest

This photo was sent to me by Christian Blohmann from the Max Planck Insitute for Mathematics in Bonn. It was taken in the hallway outside his office, which is often used by passers-by on their way to and from seminars, afternoon tea, etc. This particular board had been used as a backdrop for an interview of Professor Don Zagier, one of the directors of MPI and a very distinguished number theorist. Christian particularly liked the photo as it shows a kind of modern mathematical palimpsest, with many different layers of mathematics on top of one another. Mathematicians would often rather pick up a different coloured pen and start writing straight away than take the time to clean the board!

## Maths and grammar

This photo was taken at the Max Planck Institute for Mathematics in Bonn, where I was invited to spend a few days this week. At 4pm every day the mathematicians there meet for tea and biscuits and mathematical discussions. After tea on Monday I found this whiteboard which really showcases the combination of serious maths, playfulness and different cultures that make MPI a great place to work in.

## The Lorentz Center gets a new board

This photo was sent in by René Pannekoek, a PhD student at the University of Leiden, saying that this wall has just been built in the Lorentz Center – a conference centre attached to Leiden University. It is in the place where their old library used to be, and this photo has captured the very first maths/doodles/obscure literary references on the new wall/board. I hope it is a sign of future exciting scribblings to come!

## Algebraic variety night

This week we have an unusual post – a video of a blackboard! This is part of a Swiss theatre production, and a translation of the blurb on their website is as follows: “In their new production, the Matterhorn company deals with mathematics. Both the content and the structure are motivated by mathematical questions. They use the Euler characteristic as an all-singing and all-dancing guiding principle in their search for mathematics. “The many folds” is a unique attempt to develop a theatrical production based on mathematical principles, and to use the stage to extend and re-interpret mathematics.”

Please let us know if you’ve seen the production!