In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, two-center bipolar coordinates is a coordinate system, based on two coordinates which give distances from two fixed centers, C₁ and C₂ This system is very useful in some scientific applications It should not be confused with so-called bipolar coordinates

Bipolar coordinates

Bipolar coordinates are a two-dimensional orthogonal coordinate system. There are two commonly defined types of bipolar coordinates. The other system is two-center bipolar coordinates. There is also a third coordinate system that is based on two poles . The first is based on the Apollonian circles...

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Cartesian coordinates

Transformation to Cartesian coordinates from two-center bipolar coordinates

where the centers of this coordinate system are at (+a, 0) and (-a, 0).

Polar coordinates

To polar coordinates from two-center bipolar coordinates

Where 2a is the distance between the poles (coordinate system centers).