Blue Gomboc Light, a mathematical innovation, self-righting shape, science toy

Description

GÖMBÖC LIGHT is the least heavy, least sensitive, least expensive Gömböc procedured so far. Its playful motion may entertain, however it can equally serve as a demonstration tool. Its special production technology is a fruit of several years of experiments.  The Gömböc is the first known convex, homogeneous obejct to have just one stable (S) and one unstable (I) equilibrium points. The Gömböc always self-rights to its single stabile position. It can be proven that no object with less than two equilibria exists.   Gömböc is a significant scientific innovation in mathematics, geology and biology as well as in art and design. There are a growing number of educational materials that contain references to the Gömböc, such as school books or learning software. There are several public places and museums where the Gömböc has already been displayed/exhibited. We believe that the Gömböc is an interesting science toy for schools, universities, exhibitions and museums.
The existence of the Gömböc was conjectured in 1995 by one of the greatest mathematicians of the 20th century, Vladimir Igorevich Arnold. The inventors of the Gömböc are Gábor Domokos and Péter Várkonyi from the Departnent of Mechanics, Materials and Structures of the Budapest University of Technology and Economics.
The Gömböc can be considered as a "mathematical stem-cell": All equilibrium classes of objects can be constructed by using the Gömböc as a starting point, but not the other way around: the existence of the Gömböc cannot be deduced from other shapes. Due to its similarity to the sphere, the Gömböc is one of the most sensitive geometric forms. Nevertheless, the organic environment managed to produce a Gömböc-like shape in the form of the shell of the Indian Star Tortoise. Moreover, in the un-organic environment (for example, among abrading pebbles) the Gömböc is the ultimate, though unattainable goal of shape evolution. This theory enabled a scientific team from Budapest, Philadelphia and NASA to decode the history of pebble shapes on Mars, gaining new, essential insight into the ancient fluvial environment on the Red Planet. The focus of the Hungarian Pavilion of the 2010 Shanghai World Expo was the Gömböc, as the symbol of harmony and creativity.
Metal Gömböc pieces are produced at much higher accuracy with computer controlled machining (CNC). Due to their extreme precision their motion (on a sufficiently smooth, clean surface) lasts much longer.
Individual, numbered pieces are manufactured at special request. Gömböc 001 was presented to Professor V.I. Arnold on his 70th birthday by the inventors. Other numbered pieces are on exhibit at world-famous institutions:
- 1000 was presented by the Hungarian Research Fund to the European Research Council
- 1209 is at the Whipple Museum of the History of Science at the University of Cambridge
- 1409 is at the Mathematical Institue of the University of Leipzig
- 1546 is at Trinity College, Cambridge
- 1737 is at the Mathematical Institute of the University of Göttingen
- 1746 is at the Mathematical Department of Princeton University
- 1785 is at the Department of Mathematics, University of Georgia
- 1802 is at the Hungarian National Museum
- 1821 is at the British Crown Estate
- 1823 is at the Bolyai Memorial Museum at Tirgu Mures (Marosvásárhely)
- 1825 is at the Hungarian Academy of Sciences
- 1855 is at Pennsylvania State University
- 1896 is at the Hungarian Patent Office
- 1910  is at the University of KwaZulu-Natal, Durban, South Africa
- 1924 is at the Hungarian National Bank
- 1928 is at the Institut Henri Poincaré in Paris
- 1988 is at University of Waterloo, Canada
- 2013 is at the Mathematical Institute of Oxford University