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Disentanglement Puzzle
Disentanglement puzzles (also called entanglement puzzles, tanglement puzzles, tavern puzzles or topological puzzles) are a type or group of mechanical puzzle that involves disentangling one piece or set of pieces from another piece or set of pieces. Several subtypes are included under this category, the names of which are sometimes used synonymously for the group: wire puzzles; nail puzzles; ring-and-string puzzles; ''et al''. Although the initial object is disentanglement, the reverse problem of reassembling the puzzle can be as hard as—or even harder than—disentanglement. There are several different kinds of disentanglement puzzles, though a single puzzle may incorporate several of these features. Wire-and-string puzzles upright=1.2, A complex ''Baguenaudier'' puzzle. The goal is to free the string. Wire-and-string puzzles usually consist of: * one piece of string, ribbon or similar, which may form a closed loop or which may have other pieces like balls fixed t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unlink
In the mathematics, mathematical field of knot theory, an unlink is a Link (knot theory), link that is equivalent (under ambient isotopy) to finitely many disjoint circles in the plane. Properties * An ''n''-component link ''L'' ⊂ S3 is an unlink if and only if there exists ''n'' disjointly embedded discs ''D''''i'' ⊂ S3 such that ''L'' = ∪''i''∂''D''''i''. * A link with one component is an unlink if and only if it is the unknot. * The link group of an ''n''-component unlink is the free group on ''n'' generators, and is used in classifying Brunnian links. Examples * The Hopf link is a simple example of a link with two components that is not an unlink. * The Borromean rings form a link with three components that is not an unlink; however, any two of the rings considered on their own do form a two-component unlink. * Taizo Kanenobu has shown that for all ''n'' > 1 there exists a hyperbolic link of ''n'' components such that a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unknotting Problem
In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major unresolved challenge is to determine if the problem admits a polynomial time algorithm; that is, whether the problem lies in the complexity class P. Computational complexity First steps toward determining the computational complexity were undertaken in proving that the problem is in larger complexity classes, which contain the class P. By using normal surfaces to describe the Seifert surfaces of a given knot, showed that the unknotting problem is in the complexity class NP. claimed the weaker result that unknotting is in AM ∩ co-AM; however, later they retracted this claim. In 2011, Greg Kuperberg proved that (assuming the generalized Riemann hypothesis) the unknotting problem is in co-NP, and in 2016, Marc Lackenby provided an unconditional pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tangloids
Tangloids is a mathematical game for two players created by Piet Hein to model the calculus of spinors. A description of the game appeared in the book ''"Martin Gardner's New Mathematical Diversions from Scientific American"'' by Martin Gardner from 1996 in a section on the mathematics of braiding.M. Gardner''Sphere Packing, Lewis Carroll, and Reversi: Martin Gardner's New Mathematical Diversions'', Cambridge University Press, September, 2009, Two flat blocks of wood each pierced with three small holes are joined with three parallel strings. Each player holds one of the blocks of wood. The first player holds one block of wood still, while the other player rotates the other block of wood for two full revolutions. The plane of rotation is perpendicular to the strings when not tangled. The strings now overlap each other. Then the first player tries to untangle the strings without rotating either piece of wood. Only translations (moving the pieces without rotating) are allowed. Aft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Human Knot
A human knot is a common icebreaker game or team building activity for new people to learn to work together in physical proximity. The knot is a disentanglement puzzle in which a group of people in a circle each hold hands with two people who are not next to them, and the goal is to disentangle the limbs to get the group into a circle, without letting go of grasped hands. Instead, group members should step over or under arms to try to untangle the knot. Not all human knots are solvable (see unknotting problem) and can remain knots or may end up as two or more circles. An easy way to ensure that the game will end up with a single circle with no nodes is to start from a circle of people holding each other hand, looking all towards the center of the circle, and ask some of them to cross his/her arms and swap his left hand with his right hand grasping again the same neighbors. When the game is successfully completed a certain number of people will appear to be outside of the circ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borromean Rings
In mathematics, the Borromean rings are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the three is cut or removed. Most commonly, these rings are drawn as three circles in the plane, in the pattern of a Venn diagram, alternatingly crossing over and under each other at the points where they cross. Other triples of curves are said to form the Borromean rings as long as they are topologically equivalent to the curves depicted in this drawing. The Borromean rings are named after the Italian House of Borromeo, who used the circular form of these rings as a coat of arms, but designs based on the Borromean rings have been used in many cultures, including by the Norsemen and in Japan. They have been used in Christian symbolism as a sign of the Trinity, and in modern commerce as the logo of Ballantine beer, giving them the alternative n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Configuration Space (physics)
In classical mechanics, the parameters that define the configuration of a system are called '' generalized coordinates,'' and the space defined by these coordinates is called the configuration space of the physical system. It is often the case that these parameters satisfy mathematical constraints, such that the set of actual configurations of the system is a manifold in the space of generalized coordinates. This manifold is called the configuration manifold of the system. Notice that this is a notion of "unrestricted" configuration space, i.e. in which different point particles may occupy the same position. In mathematics, in particular in topology, a notion of "restricted" configuration space is mostly used, in which the diagonals, representing "colliding" particles, are removed. Example: a particle in 3D space The position of a single particle moving in ordinary Euclidean 3-space is defined by the vector q=(x,y,z), and therefore its ''configuration space'' is Q=\mathbb^3. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typically ductile (can be drawn into wires) and malleable (they can be hammered into thin sheets). These properties are the result of the ''metallic bond'' between the atoms or molecules of the metal. A metal may be a chemical element such as iron; an alloy such as stainless steel; or a molecular compound such as polymeric sulfur nitride. In physics, a metal is generally regarded as any substance capable of conducting electricity at a temperature of absolute zero. Many elements and compounds that are not normally classified as metals become metallic under high pressures. For example, the nonmetal iodine gradually becomes a metal at a pressure of between 40 and 170 thousand times atmospheric pressure. Equally, some materials regarded as metals c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Puzzle
A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces in which the solution is to manipulate the whole object or parts of it. While puzzles of this type have been in use by humanity as early as the 3rd century BC, one of the most well-known mechanical puzzles of modern day is the Rubik's Cube, invented by the Hungarian architect Ernő Rubik in 1974. The puzzles are typically designed for a single player, where the goal is for the player to see through the principle of the object, rather than accidentally coming up with the right solution through trial and error. With this in mind, they are often used as an intelligence test or in problem solving training. History The oldest known mechanical puzzle comes from Greece and appeared in the 3rd century BC. The game consists of a square divided into 14 parts, and the aim was to create different shapes from these pieces. This is not easy to do. (see Ostomachion loculus Archimedius) In Iran "puzzle- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horseshoe
A horseshoe is a fabricated product designed to protect a horse hoof from wear. Shoes are attached on the palmar surface (ground side) of the hooves, usually nailed through the insensitive hoof wall that is anatomically akin to the human toenail, although much larger and thicker. However, there are also cases where shoes are glued. Horseshoes are available in a wide variety of materials and styles, developed for different types of horse and for the work they do. The most common materials are steel and aluminium, but specialized shoes may include use of rubber, plastic, magnesium, titanium, or copper.Price, Steven D. (ed.) ''The Whole Horse Catalog: Revised and Updated'' New York:Fireside 1998 , pp. 84–87. Steel tends to be preferred in sports in which a strong, long-wearing shoe is needed, such as polo, eventing, show jumping, and western riding events. Aluminium shoes are lighter, making them common in horse racing where a lighter shoe is desired, and often facilitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wire
Overhead power cabling. The conductor consists of seven strands of steel (centre, high tensile strength), surrounded by four outer layers of aluminium (high conductivity). Sample diameter 40 mm A wire is a flexible strand of metal. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Wire gauges come in various standard sizes, as expressed in terms of a gauge number. Wires are used to bear mechanical loads, often in the form of wire rope. In electricity and telecommunications signals, a "wire" can refer to an electrical cable, which can contain a "solid core" of a single wire or separate strands in stranded or braided forms. Usually cylindrical in geometry, wire can also be made in square, hexagonal, flattened rectangular, or other cross-sections, either for decorative purposes, or for technical purposes such as high-efficiency voice coils in loudspeakers. Edge-wound coil springs, such as the Slinky toy, are made of special flatten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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