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bipolar coordinates

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  • Bipolar coordinates — are a two dimensional orthogonal coordinate system. There are two commonly defined types of bipolar coordinates. [http://bbs.sachina.pku.edu.cn/Stat/Math World/math/b/b233.htm Eric W. Weisstein, Concise Encyclopedia of Mathematics CD ROM, Bipolar …   Wikipedia

  • Two-center bipolar coordinates — In mathematics, two center bipolar coordinates is a coordinate system, based on two coordinates which give distances from two fixed centers, C1 and C2 mathworld|urlname=BipolarCoordinates|title=Bipolar coordinates] This system is very useful in… …   Wikipedia

  • Bipolar cylindrical coordinates — are a three dimensional orthogonal coordinate system that results from projecting the two dimensional bipolar coordinate system in theperpendicular z direction. The two lines of foci F {1} and F {2} of the projected Apollonian circles are… …   Wikipedia

  • Bipolar — is a term used to define things with two (usually opposing) poles. It can refer to:In Medicine * Bipolar disorder and its subtypes: ** Bipolar I ** Bipolar II ** Cyclothymia * Bipolar cell, a second order neuron of the retina.In charitable… …   Wikipedia

  • Curvilinear coordinates — Curvilinear, affine, and Cartesian coordinates in two dimensional space Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian… …   Wikipedia

  • Orthogonal coordinates — In mathematics, orthogonal coordinates are defined as a set of d coordinates q = (q1, q2, ..., qd) in which the coordinate surfaces all meet at right angles (note: superscripts are indices, not exponents). A coordinate surface for a particular… …   Wikipedia

  • Oblate spheroidal coordinates — Figure 1: Coordinate isosurfaces for a point P (shown as a black sphere) in oblate spheroidal coordinates (μ, ν, φ). The z axis is vertical, and the foci are at ±2. The red oblate spheroid (flattened sphere) corresponds to μ=1, whereas the blue… …   Wikipedia

  • Paraboloidal coordinates — are a three dimensional orthogonal coordinate system (λ,μ,ν) that generalizes the two dimensional parabolic coordinate system. Similar to the related ellipsoidal coordinates, the paraboloidal coordinate system has orthogonal quadratic coordinate… …   Wikipedia

  • Ellipsoidal coordinates — are a three dimensional orthogonal coordinate system (λ,μ,ν) that generalizes the two dimensional elliptic coordinate system. Unlike most three dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces, the ellipsoidal… …   Wikipedia

  • Conical coordinates — Coordinate surfaces of the conical coordinates. The constants b and c were chosen as 1 and 2, respectively. The red sphere represents r=2, the blue elliptic cone aligned with the vertical z axis represents μ=cosh(1) and the yellow elliptic cone… …   Wikipedia

  • Toroidal coordinates — are a three dimensional orthogonal coordinate system that results from rotating the two dimensional bipolar coordinate system about the axis that separates its two foci. Thus, the two foci F {1} and F {2} in bipolar coordinates become a ring of… …   Wikipedia

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