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Not mentioned on the Aperiodical, 3/4/15

Here’s a round-up of some mathematical news from last month.

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.

Math/Maths 86: Complex Pony Tails

A new episode of the Math/Maths Podcast has been released.

A conversation about mathematics between the UK and USA from This week Samuel and Peter spoke about: The Recent Difficulties with RSA; Do we need a maths museum?; Brian Schmidt’s Mathematical Arguement; IBM claims most PhD mathematicians in its employ; Maths grads teaching alert; John Nash’s Letters to the NSA; The mathematical equation that caused the banks to crash; Rapunzel’s Number: Science behind ponytail revealed; EPSRC Shaping Capabilities; Maths Jam; & more.

Get this episode: “Math/Maths 86: Complex Pony Tails