Gömböc

An interesting mathematical curiosity: the Gömböc (pronounced "gəmbəts"). This is an intriguing object, devised by Hungarian mathematicians Gábor Domokos and Péter Várkonyi, that has the property of self-righting to a single stable position despite being homogeneous, completely convex and not being obviously "flat" or "thin".
As with many other shapes with useful mechanical properties, this self-righting behaviour has already been achieved in nature in animals such as the Indian Star Tortoise. More on this at the Mathematical Intelligencer article Mono-monostatic bodies: the answer to Arnold's question (PDF). The question of whether it is possible to construct a three dimensional body which is mono-monostatic but also homogeneous and convex was raised by the by Russian mathematician Vladimir Arnold. This is of interest because it is known to be impossible in two dimensions.
A gömböc is, incidentally, Hungarian for a round thing, which may apply to dumplings or the sinister pork haggis in the Hungarian folktale A kis gömböc that hangs in a cottage attic and eats a family.

Compare the rattleback or celt, an object of no discernable application, but one also with unusual dynamic properties: in its case, a preferred direction of spin.

source Apothecary's Drawer Weblog