My Erdős number…

…appears to be four (an infinite improvement). I coauthored a paper with Gary Greaves, whose recent paper Edge-signed graphs with smallest eigenvalue greater than -2 also saw contributions from Jack Koolen and Akhiro Munemasa. They both have an Erdős number of two (each via Chris Godsil, who is an Erdős coauthor), making Gary a three …

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What is a buckyball? Part 3: Fullerenes

In the previous post we saw how we could project polyhedra into the plane, and use some simple properties about planar graphs to classify all the possible Platonic solids. In this post we’ll finally get to the buckyball, by considering a less restrictive class of polyhedra: the fullerenes. The Platonic solids were extremely regular: every …

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What is a Buckyball? Part 2: Projection

How can we represent a 3-dimensional object such a cube in only 2-dimensions, such as on a flat piece of paper? This is the problem of projection, and it inevitably introduces inaccuracies. Different choices of perspective will alter what features survive the projection process. For instance, a perfect cube has all faces square, with corner …

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What is a Buckyball? Part 1: Planar Graphs

Earlier this year I was involved with the construction of the `Giant 4D Buckyball‘, as part of the University of Edinburgh’s Innovative Learning Week. The sculpture was actually of something rather more complicated – the Cantitruncated 600-cell – but buckyballs (in various representations) were a fundamental building block. So, what exactly are they? Julia’s description …

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2014 Joint Mathematics Meetings Art Exhibition

Some of my work will once again be included in the art exhibition at the Joint Mathematics Meetings- a selection of stills from my video project x<–>t, which I described on my main site here. The image above is a more recent rendering using the same ‘strip photography’ technique: it captures the changing behaviour through …

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The benign dictatorship of the London Underground

Earlier today I spotted this video, featuring the stand-up mathematician Matt Parker and all-round interesting person Tom Scott exploring some oddities of the tube: Matt’s ability to beat Tom around the network depended on local knowledge of hidden shortcuts. You might wonder why these quicker options aren’t indicated by signs, but as they explain in …

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JMM 2013 Highlights

Earlier this month I attended the 2013 Joint Mathematics Meetings, trading freezing Britain for sunny San Diego! This was the 119th annual meeting of the American Mathematical Society, the 96th of the Mathematical Association of America, my third trip to the US for a JMM, and the first at which I’ve given a talk. There …

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The Smoothness Spiral

I’d recently ordered Ben Fry‘s Visualizing Data and started reading it this weekend; just a few pages in I learnt how to import data to processing and a project was born… Since New Orleans I’ve been increasingly interested in mathematical art, and whether in particular I could create something interactive. Here’s what I’ve come up …

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