The Gömböc in a Nutshell What is the essence of the Gömböc? The Gömböc is the first known convex, homogeneous object to have just one stable and one unstable equilibrium point. Such objects are called mono-monostatic; and the Gömböc is the fi st known mono-monostatic object: it is a new geometric shape. It is easy to prove that objects with less than two equilibria do not exist. The Gömböc as a mathematical stem-cell It was proven that the existence of objects in every equilibrium class can be deduced from the existence of the Gömböc. Moreover, all other classes can be physically constructed by using the Gömböc as a starting point.The inverse is not true: the existence of the Gömböc could not be deduced from the existence of other shapes.There is a close analogy to stem-cells in molecular biology: other cell types can be produced from stem-cells, on the other hand, stem-cells cannot be reproduced from more differentiated other cells. The Gömböc in Nature Because of 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 inorganic environment (for example, among abrading pebbles) the Gömböc is the ultimate, though the unattainable goal of shape evolution. This theory enabled a scientific team from Budapest, from the University of Pennsylvania and from NASA to decode the history of pebble shapes on Mars, gaining new, essential insight into the ancient fluvial environment on the Red Planet. The Gömböc and the Sphere The flatness F and thinness T of any object can be measured mathematically by a numerical value greater than or equal to one (F≥1, T≥1). In the case of a sphere we have F=T=1. An object is said to be in class {S,U} if it has S stable equilibrium points and U unstable equilibrium points. It can be proven that if S>1 then F>1 and if U>1 then T>1. However, if S=U=1 (i.e. the object is a Gömböc) then it has been proven that F=T=1 (so a Gömböc can be neither flat nor thin). Since only the sphere and the Gömböc share this geometric property, we may call the Gömböc the most sphere-like object.
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