Show your mathematics to the world!

A mathematician's blackboard can evoke feelings of wonder, beauty, awe, confusion and curiosity. Send me photos of your black (or white!) board, what's on it and why you think it's interesting.

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Shape optimization

Blackboard at ICMS June 2015

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

LaFayette-April2015I 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.

Combinatorics of non-crossing partitions

Iain Gordon whiteboard
The board is a result of of Bin Shu from East China Normal University visiting Iain Gordon at the University of Edinburgh. In Iain’s words: “We were discussing the combinatorics of non-crossing partitions, and its generalisations to a bunch of different finite groups. The two diagrams are Cayley graphs of symmetric groups where one calculates this combinatorics. Most of that text is in black, but we were lazybones, so there is also a bit of green writing from my PhD student, about braid group actions on tensor categories and their asymptotic limits. Amazingly, the two topics are linked, through moduli spaces in algebraic geometry!”

Board of pi

IMG_20150319_170705

This board by David Cushing at Newcastle University attempts to calculate pi very crudely by counting how many squares a circle covers and using the formula

Area = pi x r2

to get a value of 2.98. Can you do better?

This exercise was part of a series of activities carried out to celebrate “Ultimate pi day” on 3/14/15 (in US date format). There were also many other attempts by people to  estimate the value of pi using nonstandard methods. Did you take part in the festivities and, if so, how?

Backward differential equations

SiskaOct2014This board was created in the common room of the School of Mathematics at the University of Edinburgh by David Siska and Arnaud Lionnet. Arnaud is visiting David in Edinburgh, and they are working on backward stochastic differential equations and stochastic partial differential equations, which are on the interface between probability and analysis.

Self-intersection numbers for a fence

whiteboard Seifert pairingThis is the board of Chris Palmer, a postgraduate at the University of Edinburgh. He has recently been working on finding a simple chain level Seifert pairing for the Seifert surface of a link. This is related to his supervisor Andrew Ranicki’s recent talk in which he used surgery theory to find a chain level pairing. The figures show how to compute the self intersection numbers for a fence (a one-dimensional simplicial complex that is a deformation retraction of the Seifert surface).

Backdrop for Sir Michael Atiyah

(c) James GlossopToday the University of Edinburgh was privileged to welcome award-winning photographer James Glossop to the School of Mathematics. His task was to photograph Sir Michael Atiyah for an article in The Times (to appear next week) and he asked for a blackboard to be decorated with mathematical equations to form the backdrop to this photo. It was a joint effort between Andrew Ranicki, Julia Collins, Patrick Orson, and (of course) Sir Michael, and contains all their favourite formulae, numbers and ideas in mathematics. What would you have drawn on the board?

James kindly took this photo of the board after he was finished getting his shots of Sir Michael. I like the heavenly light shining in from above!

Niels Bohr Institute

Copenhagen Niels Bohr Institute blackboard

This is the blackboard in the common room at the Niels Bohr Institute in Copenhagen, taken by Andrew Jackson. It is advertising a colloquium given by Julia Collins about Peter Guthrie Tait, with a helpful diagram of a vortex cannon to show people what to expect in the talk.  Unrelatedly, there is a lot of matrix algebra on the left and what seems to be a half-rubbed-off torus on the right. Proof that even in a physics institute, much of the work is really mathematics! We have no idea what the cartoon at the top signifies.

Inverse blackboard

Inverse blackboard Christian Perfect and David Cushing spent the morning computing inverses using their special inverse blackboard.

Going left-to-right and top-to-bottom, we have:

  • The inverse of a 2×2 matrix;
  • The commutative diagram for the universal property of the inverse limit;
  • A variable which is inversely proportional to another;
  • The inverse of a complex number;
  • The derivative of the inverse of a function;
  • The inverse tangent of 1;
  • The axiom for group inverses;
  • Part of the definition of the logical inverse.

Thanks Christian and David for this wonderful idea!

 

Doors Open Day

Blackboard from ICMSOn 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?

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