TORONTO STAR (Ontario) 24 October 07 Winners in the old shell game; A mathematician has found why only a lucky few species of turtles can right themselves after being flipped. It all depends on the shape of the shell (Peter Calamai)

Flip a few special kinds of turtles on their backs and they'll automatically flip back upright by using the pull of gravity, just like the wobbling Weebles children's toys.

Their secret lies in a rare geometric shape identified for the first time after a decade-long quest by a Hungarian mathematician who had no initial interest in turtles.

Most turtles try to recover from being overturned by pushing against the ground with their necks and feet or by prying against something like a rock. And they don't always succeed, falling victim to predators or death by starvation and drying out.

But not the few species of high-domed land turtles - also called tortoises - blessed with what Gabor Domokos calls a monostatic shape. "No matter how you put a monostatic object down it will always rearrange itself to the same unique position," says the math professor at Budapest University of Technology and Economics.

That means safely back on its feet for creatures like the brightly patterned Indian star tortoise, popular in the exotic pet trade.

Domokos and graduate student Peter Varkonyi tested the theory by overturning more than three dozen star tortoises. Almost all spontaneously flipped right side up, sometimes after a little foot waggling.

The two mathematicians began flipping turtles after designing a self- righting object that was homogenous, unlike the Weebles which are weighted in the bottom. Called a Gomboc, the object is like a ball that's been pinched so it has a flattish bottom and a high back.

Once the two mathematicians came up with the Gomboc, however, they immediately spotted the close resemblance to some tropical land tortoises with high backs.

No more than 10 of the world's 200 known species of sea and land turtles are self-righting.
Winners in the old shell game

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