A mathematical problem in which you can hold the proof physically in your own hands - the world’s first
self-righting object.
The Gomboc is a roundish piece of clear synthetic material with
gently peaked, organic curves. It looks like a piece of modern art. But
if you tip it over, something unusual happens: it rights itself.
It leans off to one side,
rocks to and fro as if gathering strength and then, presto, tips itself
back into a “standing” position as if by magic. It doesn’t have a
hidden counterweight inside that helps it perform this trick, like an
inflatable punching-bag doll that uses ballast to bob upright after you
whack it. No, the Gomboc is something new: the world’s first
self-righting object.
The Gomboc is a result of a long
mathematical quest. In 1995, the Russian mathematician Vladimir Arnold
mused that it would be possible to create a “mono-monostatic” object —
a three-dimensional thingy that purely by dint of its geometry had only
one possible way to balance upright.
The challenge intrigued two
scientists — Gabor Domokos and Peter Varkonyi, both of the Budapest
University of Technology and Economics. They spent a few years doing
the math, and it seemed as if a mono-monostatic object could, in fact,
exist. They began looking to see if they could find a naturally
occurring example; at one point, Domokos was so obsessed that he spent
hours testing 2,000 pebbles on a beach to see if they could right
themselves. (None could.)
After several more years of
scratching their heads, they finally hit upon a shape that looked
promising. They designed it on a computer, and when it came back from
the manufacturer, they nervously tipped it over, wondering if all their
work would be for naught. Nope: the Gomboc performed perfectly. “It’s a
very nice mathematical problem because you can hold the proof in your
hands — and it’s quite beautiful,” Varkonyi says.
Yet the
scientists now say that Mother Nature may have beaten them in the race
after all. They have noticed that the Gomboc closely resembles the
shell of a tortoise or a beetle, creatures whose round-shelled backs
help them right themselves when flipped over. “We discovered it with
mathematics,” Domokos notes, “but evolution got there first.”
Via the NY Times