“A shape whose impossibility might have been an elegant theorem, but whose existence may be much more elegant.”

– Chandler-Davis, editor-in-chief, The Mathematical Intelligencer

Presenting: The Gomboc!

I’m no mathematician, but this is cool. The Gomboc is the world’s first mono-monostatic (self-righting) three-dimensional convex homogeneous object. It has one stable and one unstable point of equilibrium. Push it over, and it gets right back up again. The existence of such an object was postulated 13 years ago by Vladimir Arnold, but no-one knew whether or not it could actually exist. Now Péter Várkonyi and Gabor Domokos have come up with such a shape, and published in The Mathematical Intelligencer. The inventors of the Gomboc note that some turtle shells are very close to a Gomboc shape, assisting the animals in self-righting. Thought they do carefully note that turtles are not actually homogeneous.

I love mathematician-speak. From their paper, “Mono-monostatic Bodies: The Answer to Arnold’s Question”:

Lemma 1 confirms our initial intuition that mono-monostatic bodies can be neither flat, nor thin. In fact, they have simultaneously minimal flatness and minimal thinness; […]

In other words, it is kinda sorta roundish.

The mathematicians examined 2000 pebbles from Greek beaches searching for mono-monostatic pebbles (the search is documented here), and found not a one:

The extreme physical fragility of these forms (i.e., their sensitivity to local perturbations due to abrasion) was also confirmed by statistical experiments on pebbles (reported in [7]); in a sample of 2000 pebbles not a single mono-monostatic object could be identified. Apparently, mono-monostatic bodies escape everyday human intuition.

They did not escape Arnold’s intuition.

The limited editions are selling for around a thousand euros right now at gomboc.eu, but how long before a mass-market version is on the shelves? Coolest. paperweight. ever.

[via Neatorama.]

Categories: Science