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  2. Polar coordinate system - Wikipedia

    en.wikipedia.org/wiki/Polar_coordinate_system

    In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

  3. Coordinate systems for the hyperbolic plane - Wikipedia

    en.wikipedia.org/wiki/Coordinate_systems_for_the...

    The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian system) is called the pole, and the ray from the pole in the reference direction is the polar axis.

  4. Coordinate system - Wikipedia

    en.wikipedia.org/wiki/Coordinate_system

    Another common coordinate system for the plane is the polar coordinate system. [7] A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).

  5. List of common coordinate transformations - Wikipedia

    en.wikipedia.org/wiki/List_of_common_coordinate...

    Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...

  6. Complex plane - Wikipedia

    en.wikipedia.org/wiki/Complex_plane

    In the Cartesian plane it may be assumed that the range of the arctangent function takes the values (−π/2, π/2) (in radians), and some care must be taken to define the more complete arctangent function for points (x, y) when x ≤ 0. [note 1] In the complex plane these polar coordinates take the form

  7. Del in cylindrical and spherical coordinates - Wikipedia

    en.wikipedia.org/wiki/Del_in_cylindrical_and...

    The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by φ ∈ [ 0 , 2 π ] {\displaystyle \varphi \in [0,2\pi ]} : it is the angle between the x -axis and the projection of the radial vector onto the xy -plane.

  8. Rotation of axes in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_of_axes_in_two...

    A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.

  9. Pole and polar - Wikipedia

    en.wikipedia.org/wiki/Pole_and_polar

    Conversely, the polar line (or polar) of a point Q in a circle C is the line L such that its closest point P to the center of the circle is the inversion of Q in C. If a point A lies on the polar line q of another point Q, then Q lies on the polar line a of A. More generally, the polars of all the points on the line q must pass through its pole Q.