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Bach's Fight For Freedom
Freedom, generally, is having an ability to act or change without constraint. A thing is "free" if it can change its state easily and is not constrained in its present state. In philosophy and religion, it is associated with having free will and being without undue or unjust constraints, or enslavement, and is an idea closely related to the concept of liberty. A person has the freedom to do things that will not, in theory or in practice, be prevented by other forces. Outside of the human realm, freedom generally does not have this political or psychological dimension. A rusty lock might be oiled so that the key has freedom to turn, undergrowth may be hacked away to give a newly planted sapling freedom to grow, or a mathematician may study an equation having many degrees of freedom
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Freedom (other)
Freedom, generally, is having an ability to change without constraint. Freedom
Freedom
may also refer to:Contents1 Philosophy 2 Companies 3 Computing 4 Transport 5 Geography 6 Arts and entertainment6.1 Animation 6.2 Books 6.3 Fictional entities 6.4 Film and television 6.5 Games 6.6 Graffiti 6.7 Music6.7.1 Albums 6.7.2 Songs6.8 Sculpture7 Mathematics and physics 8 Press 9 Sports 10 Other 11 See alsoPhilosophy[edit]Free will Rights Civil liberties Political freedom
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space
Euclidean space
near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space
Euclidean space
of dimension n. In this more precise terminology, a manifold is referred to as an n-manifold. One-dimensional manifolds include lines and circles, but not figure eights (because they have crossing points that are not locally homeomorphic to Euclidean 1-space). Two-dimensional manifolds are also called surfaces
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Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown. Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation. A typical example is the quadratic formula, which allows one to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation to the variables that represent them. The concept of a variable is also fundamental in calculus. Typically, a function y = f(x) involves two variables, y and x, representing respectively the value and the argument of the function
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Six Degrees Of Freedom
Six degrees of freedom
Six degrees of freedom
(6DoF) refers to the freedom of movement of a rigid body in three-dimensional space. Specifically, the body is free to change position as forward/backward (surge), up/down (heave), left/right (sway) translation in three perpendicular axes, combined with changes in orientation through rotation about three perpendicular axes, often termed yaw (normal axis), pitch (lateral axis), and roll (longitudinal axis).Contents1 Robotics 2 Engineering 3 Operational envelope types 4 Game controllers 5 See also 6 ReferencesRobotics[edit] Serial and parallel manipulator systems are generally designed to position an end-effector with six degrees of freedom, consisting of three in translation and three in orientation
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Degrees Of Freedom (mechanics)
In physics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration. It is the number of parameters that determine the state of a physical system and is important to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering. The position of a single railcar (engine) moving along a track has one degree of freedom because the position of the car is defined by the distance along the track. A train of rigid cars connected by hinges to an engine still has only one degree of freedom because the positions of the cars behind the engine are constrained by the shape of the track. An automobile with highly stiff suspension can be considered to be a rigid body traveling on a plane (a flat, two-dimensional space). This body has three independent degrees of freedom consisting of two components of translation and one angle of rotation
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Mechanism (engineering)
A mechanism, in engineering, is a device that transforms input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components that can include:Gears and gear trains Belt and chain drives Cam
Cam
and followers linkage Friction devices, such as brakes and clutches Structural components such as a frame, fasteners, bearings, springs, lubricants Various machine elements, such as splines, pins, and keys[1]The German scientist Reuleaux[2] provides the definition "a machine is a combination of resistant bodies so arranged that by their
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Motor Control
Motor control
Motor control
is the process by which humans and animals use their brain/cognition to activate and coordinate the muscles and limbs involved in the performance of a motor skill. Fundamentally, it is the integration of sensory information, both about the world and the current state of the body, to determine the appropriate set of muscle forces and joint activations to generate some desired movement or action
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Degrees Of Freedom Problem
The degrees of freedom problem or motor equivalence problem in motor control states that there are multiple ways for humans or animals to perform a movement in order to achieve the same goal
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Mathematics
Mathematics
Mathematics
(from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity,[1] structure,[2] space,[1] and change.[3][4][5] It has no generally accepted definition.[6][7] Mathematicians seek out patterns[8][9] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist
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Dimension (mathematics And Physics)
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.[1][2] Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism
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Algebraic Variety
Algebraic varieties are the central objects of study in algebraic geometry. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition.[1]:58 Conventions regarding the definition of an algebraic variety differ slightly. For example, some definitions require an algebraic variety to be irreducible, which means that it is not the union of two smaller sets that are closed in the Zariski topology. Under this definition, non-irreducible algebraic varieties are called algebraic sets. Other conventions do not require irreducibility. The concept of an algebraic variety is similar to that of an analytic manifold
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Intellectual Freedom
Intellectual freedom encompasses the freedom to hold, receive and disseminate ideas without restriction.[1] Viewed as an integral component of a democratic society, intellectual freedom protects an individual's right to access, explore, consider, and express ideas and information as the basis for a self-governing, well-informed citizenry
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Degrees Of Freedom (physics And Chemistry)
In physics, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all dimensions of a system is known as a phase space, and degrees of freedom are sometimes referred to as its dimensions.Contents1 Definition 2 Gas molecules 3 Independent degrees of freedom 4 Quadratic degrees of freedom4.1 Quadratic and independent degree of freedom 4.2 Equipartition theorem5 Generalizations 6 ReferencesDefinition[edit] A degree of freedom of a physical system is an independent parameter that is necessary to characterize the state of a physical system. In general, a degree of freedom may be any useful property that is not dependent on other variables. The location of a particle in three-dimensional space requires three position coordinates. Similarly, the direction and speed at which a particle moves can be described in terms of three velocity components, each in reference to the three dimensions of space
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Physics
Physics
Physics
(from Ancient Greek: φυσική (ἐπιστήμη), translit. physikḗ (epistḗmē), lit. 'knowledge of nature', from φύσις phýsis "nature"[1][2][3]) is the natural science that studies matter[4] and its motion and behavior through space and time and that studies the related entities of energy and force.[5] Physics
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Chemistry
Chemistry
Chemistry
is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.[1][2] Chemistry
Chemistry
addresses topics such as how atoms and molecules interact via chemical bonds to form new chemical compounds. There are four types of chemical bonds: covalent bonds, in which compounds share one or more electron(s); ionic bonds, in which a compound donates one or more electrons to another compound to produce ions: cations and anions; hydrogen bonds; and Van der Waals force
Van der Waals force
bonds
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