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Anyone who hasn’t yet spotted the YouTube channel Numberphile (call yourself a maths fan?) would do well to check out its amazing selection of videos, all loosely themed around numbers – not all of which are integers, either – but now edging on giving up on that pretence and just continuing to post videos about interesting bits of maths.

Dance Your PhD: Cutting Sequences on the Double Pentagon

As a mathematician (and not just any kind of mathematician – a PURE mathematician), I heard of the “Dance Your PhD” contest and immediately burst out laughing. As much as there is some nice pure mathematical dancing out there (see, for instance, this series of videos of different numerical sorting algorithms interpreted through dance), the idea that someone’s mathematical PhD research could be conveyed via bodily gyration was both fantastical and hilarious.

Leap Second 30 June 2012

In case you missed it, here is the leap second moment. I loaded several web and desktop clock displays. Notice how many of them didn’t take account of the extra second – but some did! For more details on what this means, see the post ‘Hang on a second‘.

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P-Value Extravaganza

This is the best video about frequentist statistics I’ve ever seen. Watch and enjoy:

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by Jesse Kelly Productions.

Found on youtube’s math blog. If that blog really is automatically generated, I think we need to reject the null hypothesis that Google hasn’t invented strong AI. Am I doing it right? brb, going to watch the video again.

Flat tori in three-dimensional space and convex integration

French researchers Vincent Borrelli, Saïd Jabrane, Francis Lazarus and Boris Thibert have described an isometric embedding of the flat torus in 3D space, using the convex integration theory developed by Gromov in the 1970s. That means they’ve produced a surface which is topologically a torus – it has a single hole — which preserves distances between points in the 4D flat torus. Interestingly, the tangent plane is defined everywhere — the surface is in a sense smooth — but the normal vector is not defined, so it’s also a fractal. This is impossible in higher dimensions

© Borrelli et al / PNAS

I’ve recorded a short video explaining in a handwavey fashion, with a few props made from things I had lying around, just what has been done.