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Hungary Pavilion features Gomboc

"CREATIVITY is the engine for humankind's progress and the core of Hungarian culture and it could also be embodied in the discovery of Gomboc - the atom of all shapes," said Richard Mohr, deputy commissioner general of the Hungarian Pavilion at World Expo 2010.

One characteristic of Hungarians is that they can always figure a way out, and that's why Hungarians have invented so many things such as ballpoint pens, telephone exchanges, the Magic Cube and now "Gomboc", said Mohr, speaking in fluent Chinese.

The colorful Magic Cube, or Rubik's Cube, has remained a popular toy since its invention 36 years ago. At the 2010 World Expo, the Hungarians are promoting another eye-catching mathematical product - Gomboc.

Like a roly-poly toy, or wobbly man, a Gomboc can right itself when pushed over.

"But there is a huge difference. A roly-poly relies on heavy things on the bottom to right itself. However, a Gomboc is made of one material: we call it homogeneous. It has only one stable balance point," said Mohr.

At the center of the Hungarian Pavilion stands a huge Gomboc shaped like a sphere but with a sharpened top. The 3-meter wide and 3-meter high object is the largest Gomboc ever made since its debut in 2006, given that the shape has strict tolerances.

"The Gomboc shape is very close to a sphere and has very strict shape tolerance - about 0.01 millimeter per 10 centimeters. Actually many stable equilibrium points would appear if the shape was changed slightly," he said.

"In the past, we knew that an object had to have at least two stable equilibrium points: for example, you can put a book this way or that way. But a Gomboc has only one stable equilibrium point: otherwise it will self-right to maintain its balance," he said.

"This is the object we know with the least stable equilibrium point: only one," he said.

"It's like when we discovered an atom, we took it as the smallest part in forming an object, but of course we discovered even smaller parts than atoms. Gomboc is like the atom of all other geometric shapes," he said.

A Gomboc is a convex, three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium.

Its existence was proposed by Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by Hungarian scientists Gabor Domokos and Peter Varkonyi.

Though it is a result of mathematical work, Gomboc-like forms already exist in nature, though they are not accurate possibly due to their high shape sensitivity.

One example is the Indian star tortoise. When turned over, the turtle can roll back easily without relying much on its limbs.


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