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Gömböc
The Gömböc ( ) is the first known physical example of a class of convex three-dimensional homogeneous bodies, called mono-monostatic, which, when resting on a flat surface have just one stable and one unstable point of equilibrium. The existence of this class was conjectured by the Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by the Hungarian scientists Gábor Domokos and Péter Várkonyi by constructing at first a mathematical example and subsequently a physical example. Mono-monostatic shapes exist in countless varieties, most of which are close to a sphere, with a stringent shape tolerance (about one part in a thousand). Gömböc is the first mono-monostatic shape which has been constructed physically. It 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 an equilibrium position after being placed upside down. Copies of the Gömböc have been donate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gömböc
The Gömböc ( ) is the first known physical example of a class of convex three-dimensional homogeneous bodies, called mono-monostatic, which, when resting on a flat surface have just one stable and one unstable point of equilibrium. The existence of this class was conjectured by the Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by the Hungarian scientists Gábor Domokos and Péter Várkonyi by constructing at first a mathematical example and subsequently a physical example. Mono-monostatic shapes exist in countless varieties, most of which are close to a sphere, with a stringent shape tolerance (about one part in a thousand). Gömböc is the first mono-monostatic shape which has been constructed physically. It 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 an equilibrium position after being placed upside down. Copies of the Gömböc have been donate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gömböc Structure
The Gömböc ( ) is the first known physical example of a class of convex three-dimensional homogeneous bodies, called mono-monostatic, which, when resting on a flat surface have just one stable and one unstable point of equilibrium. The existence of this class was conjectured by the Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by the Hungarian scientists Gábor Domokos and Péter Várkonyi by constructing at first a mathematical example and subsequently a physical example. Mono-monostatic shapes exist in countless varieties, most of which are close to a sphere, with a stringent shape tolerance (about one part in a thousand). Gömböc is the first mono-monostatic shape which has been constructed physically. It 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 an equilibrium position after being placed upside down. Copies of the Gömböc have been donat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gömböc Statue
The Gömböc ( ) is the first known physical example of a class of convex three-dimensional homogeneous bodies, called mono-monostatic, which, when resting on a flat surface have just one stable and one unstable point of equilibrium. The existence of this class was conjectured by the Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by the Hungarian scientists Gábor Domokos and Péter Várkonyi by constructing at first a mathematical example and subsequently a physical example. Mono-monostatic shapes exist in countless varieties, most of which are close to a sphere, with a stringent shape tolerance (about one part in a thousand). Gömböc is the first mono-monostatic shape which has been constructed physically. It 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 an equilibrium position after being placed upside down. Copies of the Gömböc have been donat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gábor Domokos
Gábor Domokos (born 12 November 1961) is a Hungarian mathematician and engineer. He is best known for his 2006 discovery of the Gömböc, a class of three-dimensional (3D) convex bodies that have one stable and one unstable point of balance. Their shape helped to relate the body structure of some tortoises and their ability to recover after being placed upside down. Career Domokos spent most of his career at the Budapest University of Technology and Economics (BME), where he received his MSc degree in architecture and engineering in 1986, and defended a PhD in 1989 and habilitation in 1996. He became a full professor at BME in 1996, and in 2002 was appointed as head of Department of Mechanics, Materials and Structures. In 1989–1999 Domokos spent one year teaching at Cornell University where he is adjunct professor of mechanical and aerospace engineering. In 2004 he has been elected as the youngest member of the Hungarian Academy of Sciences – first as a corresponding mem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weeble
Weebles is a range of children's roly-poly toys originating in the US in Hasbro's Playskool division on July 23, 1971. Tipping an egg (biology), egg-shaped Weeble causes a weight located at the bottom-center to be lifted off the ground. Once released, gravity brings the Weeble back into an upright position. Weebles have been designed with a variety of shapes, including some designed to look like people or animals. The catchphrase "Weebles wobble, but they don't fall down" was used in advertising during their rise in popularity in the 1970s and during successive relaunches in the early 2000s. The line was coined by advertising executive Walter Cohen. Walter Cohen created the phrase when he and his partner Bernard Most, were assigned to the account at Benton & Bowles (B&B) in 1971. Walter and Bernard (as the creative team Bernie & Walter) used the phrase when they created the first TV commercials for the new Hasbro product, Weebles. Mitch Reed was the account executive assigned to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gomboc2
Gomboc may refer to: Mathematics * Gömböc, a convex three-dimensional body that has one stable and one unstable point of equilibrium People * Andreja Gomboc (born 1969), Slovenian astrophysicist * Adrian Gomboc (born 1995), Slovenian judoka * Ron Gomboc Ratimir Marijan "Ron" Gomboc is an Australian sculptor. Biography Gomboc was born in 1947 in Ljubljana, Slovenia, Yugoslavia and received his early schooling in the town of Novi Vinodolski, Croatia. At the age of 13 he emigrated to Australia w ... (born 1947), Slovenian-born Australian sculptor {{disambiguation, surname Slovene-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four-vertex Theorem
The four-vertex theorem of geometry states that the curvature along a simple, closed, smooth plane curve has at least four local extrema (specifically, at least two local maxima and at least two local minima). The name of the theorem derives from the convention of calling an extreme point of the curvature function a vertex. This theorem has many generalizations, including a version for space curves where a vertex is defined as a point of vanishing torsion. Definition and examples The curvature at any point of a smooth curve in the plane can be defined as the reciprocal of the radius of an osculating circle at that point, or as the norm of the second derivative of a parametric representation of the curve, parameterized consistently with the length along the curve. For the vertices of a curve to be well-defined, the curvature itself should vary continuously, as happens for curves of smoothness C^2. A vertex is then a local maximum or local minimum of curvature. If the curvature ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monostatic Polytope
In geometry, a monostatic polytope (or unistable polyhedron) is a ''d''-polytope which "can stand on only one face". They were described in 1969 by J.H. Conway, M. Goldberg, R.K. Guy and K.C. Knowlton. The monostatic polytope in 3-space constructed independently by Guy and Knowlton has 19 faces. In 2012, Andras Bezdek discovered an 18 face solution, and in 2014, Alex Reshetov published a 14 face object. Definition A polytope is called monostatic if, when filled homogeneously, it is stable on only one facet. Alternatively, a polytope is monostatic if its centroid (the center of mass) has an orthogonal projection in the interior of only one facet. Properties * No convex polygon in the plane is monostatic. This was shown by V. Arnold via reduction to the four-vertex theorem. * There are no monostatic simplices in dimension up to 8. In dimension 3 this is due to Conway. In dimension up to 6 this is due to R.J.M. Dawson. Dimensions 7 and 8 were ruled out by R.J.M. Dawson, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roly-poly Toy
A roly-poly toy, round-bottomed doll, tilting doll, tumbler, wobbly man, or wobble doll is a round-bottomed toy, usually egg-shaped, that tends to right itself when pushed at an angle, and does this in seeming contradiction to how it should fall. The toy is typically hollow with a weight inside the bottom hemisphere. The placement of this weight is such that the toy has a center of mass below the center of the hemisphere, so that any tilting raises the center of mass. When such a toy is pushed over, it wobbles for a few moments while it seeks the upright orientation, which has an equilibrium at the minimum gravitational potential energy. Different toy manufacturers and different cultures have produced different-looking roly-poly toys: the ''okiagari-koboshi'' and some types of Daruma doll of Japan, the ''nevаlyashka'' ("untopply") or ''van'ka-vstan'ka'' ("Ivan-get-up") of Russia, and Playskool's Weebles. Japanese ''okiagari'' means "to get up (''oki'') and arise (''agari'')"; the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Arnold
Vladimir Igorevich Arnold (alternative spelling Arnol'd, russian: link=no, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, algebra, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory, including posing the ADE classification problem, since his first main result—the solution of Hilbert's thirteenth problem in 1957 at the age of 19. He co-founded two new branches of mathematics— KAM theory, and topological Galois theory (this, with his student Askold Khovanskii). Arnold was also known as a popularizer of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as the famous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects every line into a single line segment (possibly empty). For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set is always a convex curve. The intersection of all the convex sets that contain a given subset of Euclidean space is called the convex hull of . It is the smallest convex set containing . A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greece
Greece,, or , romanized: ', officially the Hellenic Republic, is a country in Southeast Europe. It is situated on the southern tip of the Balkans, and is located at the crossroads of Europe, Asia, and Africa. Greece shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, and Turkey to the northeast. The Aegean Sea lies to the east of the Geography of Greece, mainland, the Ionian Sea to the west, and the Sea of Crete and the Mediterranean Sea to the south. Greece has the longest coastline on the Mediterranean Basin, featuring List of islands of Greece, thousands of islands. The country consists of nine Geographic regions of Greece, traditional geographic regions, and has a population of approximately 10.4 million. Athens is the nation's capital and List of cities and towns in Greece, largest city, followed by Thessaloniki and Patras. Greece is considered the cradle of Western culture, Western civilization, being the birthplace of Athenian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
