翻訳と辞書 Words near each other ・ Gölpınar, Adıyaman ・ Gölsdorf ・ Gölsdorf axle ・ Gölsen ・ Göltarla ・ Göltarla, Elmalı ・ Göltarla, Samsat ・ Göltzsch ・ Göltzsch Viaduct ・ Gölyaka ・ Gölyeri ・ Gölyurt, Gerger ・ Gölä ・ Gölçük toothcarp ・ Gömbe, Kaş ・ Gömböc ・ Gömda ・ Gömeç ・ Göming ・ Gömlekhisar, Vezirköprü ・ Gömmaren ・ Gömmaren Nature Reserve ・ Gömmece ・ Gömmece, Kastamonu ・ Gömmece, Tarsus ・ Gömör és Kis-Hont County ・ Gömöri trichrome stain ・ Gömörszőlős ・ Gömü, Amasra ・ Gömü, Emirdağ Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gömböc ： ウィキペディア英語版 Gömböc A gömböc or 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 conjectured by Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by Hungarian scientists Gábor Domokos and Péter Várkonyi. The gömböc shape is not unique; it has countless varieties, most of which are very close to a sphere and all have very strict shape tolerance (about 0.1 mm per 100 mm). The most famous solution has a sharpened top, as shown in the photo. Its shape helped to explain the body structure of some tortoises in relation to their ability to return to equilibrium position after being placed upside down.〔〔〔〔 Copies of gömböc have been donated to institutions and museums, and the biggest one was presented at the World Expo 2010 in Shanghai, China.〔(Hungary Pavilion features Gomboc ), 12 July 2010〕〔(New geometric shape "Gomboc" featured at Shanghai Expo ), English.news.cn, 19 August 2010〕 ==History== In geometry, a body with a single stable resting position is called ''monostatic'', and the term ''mono-monostatic'' has been coined to describe a body which additionally has only one unstable point of balance. (The previously known monostatic polyhedron does not qualify, as it has three unstable equilibria.) A sphere weighted so that its center of mass is shifted from the geometrical center is a mono-monostatic body. A more common example is the Comeback Kid, Weeble or roly-poly toy (see left figure). Not only does it have a low center of mass, but it also has a specific shape. At equilibrium, the center of mass and the contact point are on the line perpendicular to the ground. When the toy is pushed, its center of mass rises and also shifts away from that line. This produces a righting moment which returns the toy to the equilibrium position. The above examples of mono-monostatic objects are necessarily inhomogeneous, that is, the density of their material varies across their body. 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 Russian mathematician Vladimir Arnold in 1995. The requirement of being convex is essential as it is trivial to construct a mono-monostatic non-convex body (an example would be a ball with a cavity inside it). Convex means that any straight line between two points on a body lies inside the body, or, in other words, that the surface has no sunken regions but instead bulges outward (or is at least flat) at every point. It was already well known, from a geometrical and topological generalization of the classical four-vertex theorem, that a plane curve has at least four extrema of curvature, specifically, at least two local maxima and at least two local minima (see right figure), meaning that a (convex) mono-monostatic object does not exist in two dimensions. Whereas a common anticipation was that a three-dimensional body should also have at least four extrema, Arnold conjectured that this number could be smaller. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gömböc」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.