News from the world of maths: A G

Wednesday, April 22, 2009

A Gömböc for Cambridge

The University of Cambridge today received a Gömböc. It was donated by its inventors Gábor Domokos and Péter Várkonyi. But what is a Gömböc and what is the University going to do with it?

A Gömböc (pronounce goemboets) is a three-dimensional body with one stable and one unstable equilibrium point. If you put it down on a horizontal surface, it will start wobbling around until it has safely reached the equilibrium position, a bit like a Weeble toy. In theory, you could balance it on the unstable equilibrium point, but in practice that's really hard because the slightest nudge will make it fall over, just like a pencil that is balancing on its tip. Unlike a Wheeble, whose self-righting ability is down to a weight in its bottom, the Gömböc is homogenous inside: its density is the same everywhere, ie there is no off-centre weight which forces it to take on a particular position. The Gömböc is also convex.

The question of whether a convex and homogenous body with one unstable and one stable equilibrium exists in three dimensions was first raised by the Russian mathematician Vladimir Arnold. Mathematicians knew before that in two dimensions there are no such shapes, and they also knew that every three-dimensional object must have at least two equilibria. Domokos and Várkonyi started working on the question and did not only prove that the Gömböc exists, but also built one. In fact, they're building many, from different materials, and they're selling them on the Gömböc website.

The Gömböc is not only beautiful and interesting, but also sheds some light on how a certain species of turtle, with a Gömböc-like shell, manages to get back on its feet after it has been toppled over. Gömböcs need to be engineered to the highest levels of precision, otherwise they won't work. The Gömböc that was today donated to the University of Cambridge can be admired at the Whipple Museum of the History of Science. Plus will interview its inventors next month and you'll be able to read the interview here soon.

You can see a Gömböc doing its thing on YouTube, though the video clip is in German.

posted by Plus @ 1:15 PM