- published: 11 Jan 2014
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A top is a toy designed to be spun rapidly on the ground, the motion of which causes it to remain precisely balanced on its tip because of inertia. Such toys have existed since antiquity. Traditionally tops were constructed of wood, sometimes with an iron tip, and would be set in motion by aid of a string or rope coiled around its axis which, when pulled quickly, caused a rapid unwinding that would set the top in motion. Today they are often built of plastic, and modern materials and manufacturing processes allow tops to be constructed with such precise balance that they can be set in motion by a simple twist of the fingers and twirl of the wrist without need for string or rope.
The motion of a top is produced in the most simple forms by twirling the stem using the fingers. More sophisticated tops are spun by holding the axis firmly while pulling a string or twisting a stick or pushing an auger. In the kinds with an auger, an internal weight rotates, producing an overall circular motion. Some tops can be thrown, while firmly grasping a string that had been tightly wound around the stem, and the centrifugal force generated by the unwinding motion of the string will set them spinning upon touching ground.
In the context of a module M over a ring R, the top of M is the largest semisimple quotient module of M if it exists.
For finite-dimensional k-algebras (k a field), if rad(M) denotes the intersection of all proper maximal submodules of M (the radical of the module), then the top of M is M/rad(M). In the case of local rings with maximal ideal P, the top of M is M/PM. In general if R is a semilocal ring (=semi-artinian ring), that is, if R/Rad(R) is an Artinian ring, where Rad(R) is the Jacobson radical of R, then M/rad(M) is a semisimple module and is the top of M. This includes the cases of local rings and finite dimensional algebras over fields.
A top is clothing that covers at least the chest, but which usually covers most of the upper human body between the neck and the waistline. The bottom of tops can be as short as mid-torso, or as long as mid-thigh. Men's tops are generally paired with pants, and women's with pants or skirts. Common types of tops are t-shirts, blouses and shirts.
The neckline is the highest line of the top, and may be as high as a head-covering hood, or as low as the waistline or bottom hem of the top. A top may be worn loose or tight around the bust or waist, and may have sleeves or shoulder straps, spaghetti straps (noodle straps), or may be strapless. The back may be covered or bare. Tops may have straps around the waist or neck, or over the shoulders.
In mathematics, four-dimensional space ("4D") is a geometric space with four dimensions. It typically is more specifically four-dimensional Euclidean space, generalizing the rules of three-dimensional Euclidean space. It has been studied by mathematicians and philosophers for over two centuries, both for its own interest and for the insights it offered into mathematics and related fields.
Algebraically, it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions. In particular a vector with four elements (a 4-tuple) can be used to represent a position in four-dimensional space. The space is a Euclidean space, so has a metric and norm, and so all directions are treated as the same: the additional dimension is indistinguishable from the other three.
In modern physics, space and time are unified in a four-dimensional Minkowski continuum called spacetime, whose metric treats the time dimension differently from the three spatial dimensions (see below for the definition of the Minkowski metric/pairing). Spacetime is not a Euclidean space.
Three-dimensional space (also: tri-dimensional space or 3-space) is a geometric three-parameter model of the physical universe (without considering time) in which all known matter exists. These three dimensions can be labeled by a combination of three chosen from the terms length, width, height, depth, and breadth. Any three directions can be chosen, provided that they do not all lie in the same plane.
In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol . This space is only one example of a great variety of spaces in three dimensions called 3-manifolds.
In mathematics, analytic geometry (also called Cartesian geometry) describes every point in three-dimensional space by means of three coordinates. Three coordinate axes are given, each perpendicular to the other two at the origin, the point at which they cross. They are usually labeled x, y, and z. Relative to these axes, the position of any point in three-dimensional space is given by an ordered triple of real numbers, each number giving the distance of that point from the origin measured along the given axis, which is equal to the distance of that point from the plane determined by the other two axes.
A five-dimensional space is a space with five dimensions. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativitistic physics. It is an abstraction which occurs frequently in mathematics, where it is a legitimate construct. In physics and mathematics, a sequence of N numbers can be understood to represent a location in an N-dimensional space. Whether or not the actual universe in which we live is five-dimensional is a topic of debate.
Much of the early work on five dimensional space was in an attempt to develop a theory that unifies the four fundamental forces in nature: strong and weak nuclear forces, gravity and electromagnetism. German mathematician Theodor Kaluza and Swedish physicist Oskar Klein independently developed the Kaluza–Klein theory in 1921, which used the fifth dimension to unify gravity with electromagnetic force. Although their approaches were later found to be at least partially inaccurate, the concept provided a basis for further research over the past century.
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Here are 10 fascinating facts about Space that will also terrify you. Like us on Facebook: https://www.facebook.com/TopTrending Follow us on Twitter: https://twitter.com/TopTrending Commentator: http://www.youtube.com/user/BaerTaffy 10 Terrifying Facts About Space
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Twitter: http://lemmi.no/twitter Facebook: http://lemmi.no/facebook Multiple sequences captured with SpaceEngine: https://www.spaceengine.org/ [Music] Puddle of Infinity - Open Sea Morning Link: https://www.youtube.com/audiolibrary/music [References & Further Reading] https://docs.google.com/spreadsheets/d/1uUFmXkfYhKiq46Hol5o_YoWrrGn2WmoaZAMS8XugkX4/pub?gid=302684451 [Thumbnail] http://lemmino.deviantart.com/art/Space-465760909
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A top is a toy designed to be spun rapidly on the ground, the motion of which causes it to remain precisely balanced on its tip because of inertia. Such toys have existed since antiquity. Traditionally tops were constructed of wood, sometimes with an iron tip, and would be set in motion by aid of a string or rope coiled around its axis which, when pulled quickly, caused a rapid unwinding that would set the top in motion. Today they are often built of plastic, and modern materials and manufacturing processes allow tops to be constructed with such precise balance that they can be set in motion by a simple twist of the fingers and twirl of the wrist without need for string or rope.
The motion of a top is produced in the most simple forms by twirling the stem using the fingers. More sophisticated tops are spun by holding the axis firmly while pulling a string or twisting a stick or pushing an auger. In the kinds with an auger, an internal weight rotates, producing an overall circular motion. Some tops can be thrown, while firmly grasping a string that had been tightly wound around the stem, and the centrifugal force generated by the unwinding motion of the string will set them spinning upon touching ground.