Impossible Gömböc reverses itself

All is well represented, as nevalyashka works : a combination of specially shaped and heavy bottom is a funny effect. But is it possible to create a facility that would have the same properties as internally homogeneous, without deposed centre of gravity? This seems unlikely, but such a body exists.

The problem nevalyashki seem trifling, yet wonders that the toys have very interesting character. So it is only one of balance and the only one of the delicate balance (in the head). Almost any other body, no matter how difficult it may be, can be sustainably deliver several ways.

Creating a homogenous body, with properties nevalyashki is this challenge mathematical minds. And, indeed, two Hungarian mathematician take up this trivial task : Gabor Domokosh (Gábor Domokos) from Budapest University of Technology and Economics (BME) and Peter Varkoni (Péter Várkonyi), now at Princeton University (Princeton University).

Is there only one form of it alone was raised after the rollover? Friends began with the permission of the tasks for the two sites, they cut out of plywood complex pieces, put them on edge and watched how they behave in overturning.

After all, the experimenters could mathematically prove that any form of a flat, at least two points of balance and a minimum of two points of unstable equilibrium.

But Gabor and Peter intended to create an improved version nevalyashki, and thus need to think about the three-dimensional objects.

They tried to extend its "two -" theory of the higher dimension and realized that the three-dimensional object samovosstanavlivayuschiysya might exist. But he will have only one point of equilibrium, and only one of the delicate balance. But the format of such a body?

First, in the search for an answer to your question, the researchers turned to nature. So Domokosh, resting in Greece during the honeymoon, tested balance 2000000 kamushkov the sea, but no copy of pebbles does not want himself "vskakivat" as nevalyashka. "Why he was still married to another question, laughing Varkoni, is not able to make each woman."

Thanks to the patience of whether Domokosha wife, or because of the talent of two mathematicians, but also bring the facility was built. First, a purely mathematical. Then fellow of the equation, which were massacred unique body.

It really only regained its strong position in overturning and turn whatever way. And he really the equilibrium point was only one, and there was only one point delicate balance.

The object called "Gömböc." A lot of people go to visit the office of Peter, where is this thing now, is not naigratsya with remarkable object. While those who understand this unique body is not a plaything.

In autumn 2006 the second Gömböc yawns on the cover of the prestigious journal Mathematical Intelligencer, Domokosh says, "the first time since 1979, by the time of the dice Rubika, Hungarian invention again ranked in the magazine.

Interestingly, after manufacture Gömböc 'and Domokosh Varkoni, and immediately thought : "something he reminds us." And quickly found a very similar object in nature. It turned out to the Indian fashion Turtle featuring unusual species.

Indeed, no turtles unwilling jams on the back. And why not give it to the evolution of nevalyashki?

However, in reality shell turtle fashion is not as perfect as Gömböc. If Turtle overturn it back, it may roll back only a small trigger feet. But then the process is completed quickly naturally, and in this respect, these turtles were better than those of their fellow other.

As once with pebbles scientists decided to check the practice of "work" for both blanket. Friends experienced "samoperevorachivaemost 30 Cyanobacteria turtles and found that many of them actually overturned on the back of the abdomen just after the very small initial push.

This, however, puzzles tel nevalyashek have not been exhausted. Researchers drew attention to the fact that Gömböc 'and the edge of the complex, skruglennuyu form. What gives him so unusual properties. But is it possible to build a homogeneous (no inside), the body that he had only flat dimensions, and that it also came after the rollover?

Hungarian experimenters were unable to find such a facility, although they put, the body can exist. And since this is not an object of our heroes sleep, they announced a prize to anyone who would find such an unusual form.

$ 10,000 divided by the number of phone lines desired. This award. Tempting? But Domokosh and Varkoni know that almost no risk. По их оценке, такое тело, если оно вообще возможно, должно обладать тысячами граней. So prize winner of a few cents. Но ведь, на самом-то деле, искателей экзотической самоуравновешивающейся формы должен привлечь вызов интеллекту.

And if the inventor is still a commercial orientation, it is able to produce its toys. "Неваляшки 2.0" (или даже 3.0, если за 2.0 посчитать Gömböc). Why not? Famous same Rubik its conundrum for the light, pre-disaster polomav head himself.