GOMBOC - Used by Nature. Proven by Mathematics. Built by 3D Printing!

As seen on the Objet blog (http://blog.objet.com/) This amazing self-righting object is the result of a long mathematical quest. It leans off to one side, rocks to and fro building up momentum until eventually, it flips itself over as if by magic - with no hidden couterweight inside. This model is printed on an Objet 3D printer, enabling the scientists at Budapest University of Technology to accurately and efficiently simulate the precise geometry determined by their mathematics.

Category:

Science & Technology

Tags:

• gomboc
• 3D printer
• 3d model
• 3d prototype
• mathematical gomboc
• self-righting object
• perpetual machine
• objet
• objet 3D printer
• mathematics
• three-dimensional object

[CherIsLovely]

"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

[CherIsLovely]

For the sphere, both are 1 as they are for Gömböc-type bodies, but for no other ones. Thus, the Gömböc is the most sphere-like body (apart from spheres). This fact inspired its Hungarian name ( 'Gömböc' is the name of a sort of traditional Hungarian butchers' product of sphere-like shape; it also appears in folk tales).

[CherIsLovely]

The Gömböc and the sphere

There is a close relationship between the Gömböc and the sphere. There are quantitative definitions of the flatness and the thinness of a given shape. According to a straightforward version of this definition, the minima of both quantities are 1.

[CherIsLovely]

The unstable equilibrium (I)

The single unstable equilibrium point of the Gömböc is on the opposite side. It is possible to balance the body in this position, however the slightest disturbance makes it fall, similar to a pencil balanced on its tip.

The question whether Gömböc-type objects exist or not was posed by the great Russian mathematician V. I. Arnold at a conference in 1995, in a conversation with Gabor Domokos.

[CherIsLovely]

The stable equilibrium (S)

If placed on a horizontal surface in an arbitrary position the Gömböc returns to the stable equilibrium point, similar to 'weeble' toys. While the weebles rely on a weight in the bottom, the Gömböc consists of homogenous material, thus the shape itself accounts for self-righting.

[CherIsLovely]

What is Gömböc (pronounced as ‘goemboets‘)?

The 'Gömböc' is the first known homogenous object with one stable and one unstable equilibrium point, thus two equilibria altogether on a horizontal surface. It can be proven that no object with less than two equilibria exists.

[Tupster]

What is so mysterious about it?