Pole and polar in the context of "Inversive geometry"

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⭐ Core Definition: Pole and polar

In geometry, a pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section.

Polar reciprocation in a given circle is the transformation of each point in the plane into its polar line and each line in the plane into its pole.

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Pole and polar in the context of Polar coordinate system

In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are

  • the point's distance from a reference point called the pole, and
  • the point's direction from the pole relative to the direction of the polar axis, a ray drawn from the pole.

The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. The pole is analogous to the origin in a Cartesian coordinate system.

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