## Board of pi

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 r^{2}

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?

## Backdrop for Sir Michael Atiyah

Today 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!

## Deformation theory and 3-folds

This photo is of the blackboard in the common room of the School of Mathematics at the University of Edinburgh. The workings on the left are by Michael Wemyss, drawn while he was talking about deformation theory (a generalization of differential calculus) with Will Donovan, as part of their work on the geometry of certain spaces, known as 3-folds. Will says, “Deformation theory lets us express the way in which a curve in a 3-fold can `move’ infinitesimally: we can then relate this to the (quantum) geometry of the 3-fold. I’ve tried to emulate Michael’s calligraphic F’s and G’s, but I haven’t had any success yet.” We don’t know who did the workings on the right.

## Portable whiteboard

This photo sent in by Colin Beveridge is not your usual whiteboard! It’s a foldaway portable whiteboard called a *Noteboard*. Find out more details at http://thisisawesome.co.uk/. Colin was using this to work on a puzzle from MathsJam: “A chopstick (a thin uniform rod) lies at rest in a smooth, hemispherical bowl. The chopstick is longer than the diameter of the bowl. What fraction of the chopstick is inside the bowl?”.

## Temple mathematics

This is the board of José Figueroa-O’Farrill at the University of Edinburgh, who is working on a project related to ‘temple mathematics’ with his Year 4 undergraduate project group. In 17th century Japan, tablets inscribed with mathematical problems would be hung in temples as gifts to the gods. The problem being discussed on this board is a plane geometry problem which appeared first in a tablet dating from 1823 in Yamagata prefecture (northern Japan). It asks to find the radius of the middle circle in terms of the radii of the two smaller circles at either side. The students will be putting these sorts of problems on posters around the maths department in Edinburgh – you can follow their efforts on their lovely website.

## Scary index theory

This board was found in Michael Singer‘s office in Edinburgh. He tells me that it was started by a student coming to him saying that they were scared of Index Theory – an understandable emotion in my opinion. The Atiyah-Singer index theorem is a powerful result which relates topological properties of a manifold with its analytical and geometric properties. [For more explanation, you could try reading my other blog post on this: http://haggisthesheep.wordpress.com/2010/09/20/heroes-of-topology/.%5D Using the theorem, Michael Singer was then able to explain a result to the student using analysis that had previously only been understood via geometry and algebra.