Bipolar coordinates
Bipolar coordinates are a two-dimensional orthogonal coordinate system based on the Apollonian circles. Confusingly, the same term is also sometimes used for two-center bipolar coordinates. There is also a third system, based on two poles (biangular coordinates). The term "bipolar" is further used on occasion 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 for systems associated with those other curves, such as elliptic coordinates.
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Apollonian circlesBiangular coordinatesBipolarBipolar CoordinateBipolar coordinateBipolar coordinate systemBipolar cylindrical coordinatesBipolar equationBispherical coordinatesCircles of ApolloniusList of circle topicsPolar plotterProblem of ApolloniusRadical axisToroidal coordinatesTwo-center bipolar coordinates
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Bipolar coordinates
Bipolar coordinates are a two-dimensional orthogonal coordinate system based on the Apollonian circles. Confusingly, the same term is also sometimes used for two-center bipolar coordinates. There is also a third system, based on two poles (biangular coordinates). The term "bipolar" is further used on occasion 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 for systems associated with those other curves, such as elliptic coordinates.
has abstract
Bipolar coordinates are a two- ...... such as elliptic coordinates.
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El sistema de coordenades bipo ...... les coordenades el·líptiques.
@ca
Las coordenadas bipolares son ...... omo las coordenadas elípticas.
@es
Les coordonnées bipolaires sont un système de coordonnées orthogonales.
@fr
Биполярные координаты — ортого ...... лярные координаты обобщаются .
@ru
Біполярна система координат — ...... декартової системи координат.
@uk
二維雙極坐標系(英語:Bipolar coordinates ...... ,即可得到雙球坐標系。繞著 y-軸旋轉,就可得到圓環坐標系。
@zh
双極座標系(そうきょくざひょうけい、英語: Bipolar ...... ことを指し、のような他の曲線に関連した座標系には使われない。
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1,026,123,366
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p/b016470
@en
title
Bipolar coordinates
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hypernym
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comment
Bipolar coordinates are a two- ...... such as elliptic coordinates.
@en
El sistema de coordenades bipo ...... es cartesianes respectivament.
@ca
Las coordenadas bipolares son ...... (las coordenadas biangulares).
@es
Les coordonnées bipolaires sont un système de coordonnées orthogonales.
@fr
Биполярные координаты — ортого ...... лярные координаты обобщаются .
@ru
Біполярна система координат — ...... декартової системи координат.
@uk
二維雙極坐標系(英語:Bipolar coordinates ...... ,即可得到雙球坐標系。繞著 y-軸旋轉,就可得到圓環坐標系。
@zh
双極座標系(そうきょくざひょうけい、英語: Bipolar ...... ことを指し、のような他の曲線に関連した座標系には使われない。
@ja
label
Bipolar coordinates
@en
Coordenadas bipolares
@es
Coordenades bipolars
@ca
Coordonnées bipolaires
@fr
Биполярная система координат
@ru
Біполярна система координат
@uk
双極座標系
@ja
雙極坐標系
@zh