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Examples Of Polar Coordinates In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.[1][2] The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the xcoordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring [...More...]  "Examples Of Polar Coordinates" on: Wikipedia Yahoo 

Coordinate (other) Coordinate may refer to:An element of a coordinate system in geometry and related domains Coordinate space in mathematics Cartesian coordinates Coordinate (vector space) Geographic coordinate system Coordinate structure in linguistics Coordinate bond Coordinate bond in chemistry Coordinate de [...More...]  "Coordinate (other)" on: Wikipedia Yahoo 

Triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted △ A B C displaystyle triangle ABC . In Euclidean geometry Euclidean geometry any three points, when noncollinear, determine a unique triangle and simultaneously, a unique plane (i.e. a twodimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher dimensional Euclidean spaces this is no longer true [...More...]  "Triangle" on: Wikipedia Yahoo 

Coordinate Surfaces In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.[1][2] The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the xcoordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring [...More...]  "Coordinate Surfaces" on: Wikipedia Yahoo 

Skew Coordinates A system of skew coordinates is a curvilinear[1] coordinate system where the coordinate surfaces are not orthogonal,[2] in contrast to orthogonal coordinates. Skew coordinates Skew coordinates tend to be more complicated to work with compared to orthogonal coordinates since the metric tensor will have nonzero offdiagonal components, preventing many simplifications in formulas for tensor algebra and tensor calculus [...More...]  "Skew Coordinates" on: Wikipedia Yahoo 

Logpolar Coordinates In mathematics, logpolar coordinates (or logarithmic polar coordinates) is a coordinate system in two dimensions, where a point is identified by two numbers, one for the logarithm of the distance to a certain point, and one for an angle [...More...]  "Logpolar Coordinates" on: Wikipedia Yahoo 

Plücker Coordinates In geometry, Plücker coordinates, introduced by Julius Plücker Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3space, P3. Because they satisfy a quadratic constraint, they establish a onetoone correspondence between the 4dimensional space of lines in P3 and points on a quadric in P5 (projective 5space). A predecessor and special case of Grassmann coordinates (which describe kdimensional linear subspaces, or flats, in an ndimensional Euclidean space), Plücker coordinates Plücker coordinates arise naturally in geometric algebra [...More...]  "Plücker Coordinates" on: Wikipedia Yahoo 

Generalized Coordinates In analytical mechanics, specifically the study of the rigid body dynamics of multibody systems, the term generalized coordinates refers to the parameters that describe the configuration of the system relative to some reference configuration. These parameters must uniquely define the configuration of the system relative to the reference configuration.[1] This is done assuming that this can be done with a single chart. The generalized velocities are the time derivatives of the generalized coordinates of the system. An example of a generalized coordinate is the angle that locates a point moving on a circle [...More...]  "Generalized Coordinates" on: Wikipedia Yahoo 

Lagrangian Mechanics Lagrangian mechanics Lagrangian mechanics is a reformulation of classical mechanics, introduced by the ItalianFrench mathematician and astronomer JosephLouis Lagrange JosephLouis Lagrange in 1788. In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms, ei [...More...]  "Lagrangian Mechanics" on: Wikipedia Yahoo 

Canonical Coordinates In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the Hamiltonian formulation of classical mechanics [...More...]  "Canonical Coordinates" on: Wikipedia Yahoo 

Hamiltonian Mechanics Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as nonHamiltonian classical mechanics. It uses a different mathematical formalism, providing a more abstract understanding of the theory [...More...]  "Hamiltonian Mechanics" on: Wikipedia Yahoo 

Barycentric Coordinates (mathematics) In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices. Coordinates also extend outside the simplex, where one or more coordinates become negative [...More...]  "Barycentric Coordinates (mathematics)" on: Wikipedia Yahoo 

Ternary Plot A ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle or de Finetti diagram is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. In population genetics, it is often called a de Finetti diagram. In game theory, it is often called a simplex plot.[1]Approximate colours of Ag–Au–Cu alloys in jewellery makingIn a ternary plot, the proportions of the three variables a, b, and c must sum to some constant, K. Usually, this constant is represented as 1.0 or 100%. Because a + b + c = K for all substances being graphed, any one variable is not independent of the others, so only two variables must be known to find a sample's point on the graph: for instance, c must be equal to K − a − b [...More...]  "Ternary Plot" on: Wikipedia Yahoo 

Trilinear Coordinates In geometry, the trilinear coordinates x:y:z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. Trilinear coordinates Trilinear coordinates are an example of homogeneous coordinates. They are often called simply "trilinears". The ratio x:y is the ratio of the perpendicular distances from the point to the sides (extended if necessary) opposite vertices A and B respectively; the ratio y:z is the ratio of the perpendicular distances from the point to the sidelines opposite vertices B and C respectively; and likewise for z:x and vertices C and A. In the diagram at right, the trilinear coordinates of the indicated interior point are the actual distances (a' , b' , c' ), or equivalently in ratio form, ka' :kb' :kc' for any positive constant k. If a point is on a sideline of the reference triangle, its corresponding trilinear coordinate is 0 [...More...]  "Trilinear Coordinates" on: Wikipedia Yahoo 

Curvilinear Coordinates In geometry, curvilinear coordinates are a coordinate system for Euclidean space Euclidean space in which the coordinate lines may be curved. Commonly used curvilinear coordinate systems include: rectangular, spherical, and cylindrical coordinate systems. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible (a onetoone map) at each point. This means that one can convert a point given in a Cartesian coordinate system Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved. Wellknown examples of curvilinear coordinate systems in threedimensional Euclidean space Euclidean space (R3) are Cartesian, cylindrical and spherical polar coordinates [...More...]  "Curvilinear Coordinates" on: Wikipedia Yahoo 

Intrinsic Equation In geometry, an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve's intrinsic properties, that is, properties that do not depend on the location and possibly the orientation of the curve. Therefore an intrinsic equation defines the shape of the curve without specifying its position relative to an arbitrarily defined coordinate system. The intrinsic quantities used most often are arc length s displaystyle s , tangential angle θ displaystyle theta , curvature κ displaystyle kappa or radius of curvature, and, for 3dimensional curves, torsion τ displaystyle tau [...More...]  "Intrinsic Equation" on: Wikipedia Yahoo 