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Vi Hart has 3D printed a hypercube made of monkeys that has the symmetries of the Quaternion group

Group theorists, often interested principally in the abstract, have been known to neglect the vital importance of producing funky gizmos that exhibit the symmetries they have theorized about. Internet maths celeb Vi Hart, working with mathematician Henry Segerman, has addressed this absence in the case of $Q_8$, the quaternion group. The object they’ve designed is four-dimensional and made of monkeys, and they’ve done the closest thing possible to making one, which is to 3D-print an embedding of it into our three-dimensional universe, also made of monkeys. Their ArXiv preprint (pdf) is well worth a read, and when you get to the photos of the resulting sculpture (entitled “More fun than a hypercube of monkeys”), you’ll fall off your chair.

Further reading

The Quaternion Group as a Symmetry Group by Vi Hart and Henry Segerman, on the ArXiv.

Nothing Is More Fun than a Hypercube of Monkeys at Roots of Unity, including an animated gif of a virtual version of the sculpture rotating through 4D-space.

Henry Segerman’s homepage

Vi Hart’s home page

App review: Incredible Numbers, by Ian Stewart

Mathematician and author Professor Ian Stewart, helped by Touch Press and his publisher Profile Books, has recently released a new app for iOS (suitable for use on an iPad) called Incredible Numbers. We saw this tweet:

and how could we resist? We borrowed a nearby iPad, downloaded the app and had a play.

How to solve a Rubik’s Cube in one easy step

Note: If you’re looking for instructions on solving Rubik’s cube from any position, there’s a good page at Think Maths.

One day some years ago I was sat at my desk idly toying with the office Rubik’s cube. Not attempting to solve it, I was just doing the same moves again and again. Particularly I was rotating one face a quarter-turn then rotating the whole cube by an orthogonal quarter-turn like this:

Having started with a solved cube, I knew eventually if I kept doing the same thing the cube would solve itself. But this didn’t seem to be happening – and I’d been doing this for some time by now. This seemed worthy of proper investigation.