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- Bipolar_coordinates abstract "Bipolar coordinates are a two-dimensional orthogonal coordinate system. There are two commonly defined types of bipolar coordinates. The first is based on the Apollonian circles. The curves of constant σ and of τ are circles that intersect at right angles. The coordinates have two foci F1 and F2, which are generally taken to be fixed at (−a, 0) and (a, 0), respectively, on the x-axis of a Cartesian coordinate system. The second system is two-center bipolar coordinates. There is also a third coordinate system that is based on two poles (biangular coordinates). The term \"bipolar\" is sometimes used to describe other curves having two singular points (foci), such as ellipses, hyperbolas, and Cassini ovals. However, the term bipolar coordinates is reserved for the coordinates described here, and never used to describe coordinates associated with those other curves, such as elliptic coordinates.".
- Bipolar_coordinates thumbnail Bipolar_isosurfaces.png?width=300.
- Bipolar_coordinates wikiPageID "1197421".
- Bipolar_coordinates wikiPageLength "7384".
- Bipolar_coordinates wikiPageOutDegree "28".
- Bipolar_coordinates wikiPageRevisionID "647692904".
- Bipolar_coordinates wikiPageWikiLink Apollonian_circles.
- Bipolar_coordinates wikiPageWikiLink Biangular_coordinates.
- Bipolar_coordinates wikiPageWikiLink Bipolar_cylindrical_coordinates.
- Bipolar_coordinates wikiPageWikiLink Bispherical_coordinates.
- Bipolar_coordinates wikiPageWikiLink Cartesian_coordinate_system.
- Bipolar_coordinates wikiPageWikiLink Cassini_oval.
- Bipolar_coordinates wikiPageWikiLink Category:Coordinate_systems.
- Bipolar_coordinates wikiPageWikiLink Coordinate_system.
- Bipolar_coordinates wikiPageWikiLink Electric_field.
- Bipolar_coordinates wikiPageWikiLink Ellipse.
- Bipolar_coordinates wikiPageWikiLink Elliptic_coordinate_system.
- Bipolar_coordinates wikiPageWikiLink Focus_(geometry).
- Bipolar_coordinates wikiPageWikiLink Helmholtz_equation.
- Bipolar_coordinates wikiPageWikiLink Hyperbola.
- Bipolar_coordinates wikiPageWikiLink Laplace_operator.
- Bipolar_coordinates wikiPageWikiLink Laplaces_equation.
- Bipolar_coordinates wikiPageWikiLink Natural_logarithm.
- Bipolar_coordinates wikiPageWikiLink Orthogonal_coordinates.
- Bipolar_coordinates wikiPageWikiLink Partial_differential_equation.
- Bipolar_coordinates wikiPageWikiLink Separation_of_variables.
- Bipolar_coordinates wikiPageWikiLink Toroidal_coordinates.
- Bipolar_coordinates wikiPageWikiLink Two-center_bipolar_coordinates.
- Bipolar_coordinates wikiPageWikiLink File:Bipolar_coordinates.png.
- Bipolar_coordinates wikiPageWikiLink File:Bipolar_isosurfaces.png.
- Bipolar_coordinates wikiPageWikiLink File:Bipolar_sigma_isosurfaces.png.
- Bipolar_coordinates wikiPageWikiLink File:Bipolar_tau_isosurfaces.png.
- Bipolar_coordinates wikiPageWikiLinkText "Bipolar coordinates".
- Bipolar_coordinates wikiPageWikiLinkText "bipolar coordinate system".
- Bipolar_coordinates wikiPageWikiLinkText "bipolar coordinates".
- Bipolar_coordinates wikiPageWikiLinkText "bipolar".
- Bipolar_coordinates id "p/b016470".
- Bipolar_coordinates title "Bipolar coordinates".
- Bipolar_coordinates wikiPageUsesTemplate Template:Orthogonal_coordinate_systems.
- Bipolar_coordinates wikiPageUsesTemplate Template:Reflist.
- Bipolar_coordinates wikiPageUsesTemplate Template:See_also.
- Bipolar_coordinates wikiPageUsesTemplate Template:Springer.
- Bipolar_coordinates subject Category:Coordinate_systems.
- Bipolar_coordinates hypernym Orthogonal.
- Bipolar_coordinates type Page.
- Bipolar_coordinates type Thing.
- Bipolar_coordinates comment "Bipolar coordinates are a two-dimensional orthogonal coordinate system. There are two commonly defined types of bipolar coordinates. The first is based on the Apollonian circles. The curves of constant σ and of τ are circles that intersect at right angles. The coordinates have two foci F1 and F2, which are generally taken to be fixed at (−a, 0) and (a, 0), respectively, on the x-axis of a Cartesian coordinate system. The second system is two-center bipolar coordinates.".
- Bipolar_coordinates label "Bipolar coordinates".
- Bipolar_coordinates seeAlso Two-center_bipolar_coordinates.
- Bipolar_coordinates sameAs Q2383591.
- Bipolar_coordinates sameAs Coordenades_bipolars.
- Bipolar_coordinates sameAs Système_de_coordonnées_bipolaires.
- Bipolar_coordinates sameAs m.04gjdd.
- Bipolar_coordinates sameAs Биполярные_координаты.
- Bipolar_coordinates sameAs Çift_kutupsal_koordinatlar.
- Bipolar_coordinates sameAs Q2383591.
- Bipolar_coordinates sameAs 雙極坐標系.
- Bipolar_coordinates wasDerivedFrom Bipolar_coordinates?oldid=647692904.
- Bipolar_coordinates depiction Bipolar_isosurfaces.png.
- Bipolar_coordinates isPrimaryTopicOf Bipolar_coordinates.