Polar coordinate system

A two-dimensional coordinate system that locates points by their distance from an origin and their angle from a reference direction. Unlike Cartesian coordinates, it represents a point by radius and angle, which can have multiple equivalent values.

Polar angle: An angle measured from a chosen reference direction to a ray or vector. It supplies the direction component of a polar coordinate.
Cartesian coordinate system: A coordinate system that locates points by signed distances along perpendicular axes. Its rectangular coordinates provide the standard comparison for polar coordinates.
Polar equation: An equation that specifies a relationship between radius and angle in a polar coordinate system. It expresses curves directly in the coordinates suited to their shape.
Rectangular coordinate system: A coordinate system that locates points by perpendicular horizontal and vertical distances. It contrasts the axis-based distances of rectangular coordinates with polar radius and angle.
Circle: The set of points in a plane at a fixed distance from a center. A circle centered at the origin is specified by a constant radius.
Euclidean distance: The straight-line distance between two points in Euclidean space. The radial coordinate measures distance from the origin.
Polar-to-Cartesian conversion: The conversion from radius and angle to horizontal and vertical coordinates using trigonometric functions. These equations turn a polar point into its Cartesian position.
Polar graph: A plotted curve whose points are specified by radius as a function of angle. It visualizes how a polar equation traces points around the origin.
Cylindrical coordinate system: A three-dimensional coordinate system using planar polar coordinates and a height coordinate. It extends the two-dimensional polar scheme by adding a vertical position.
Cardioid: A heart-shaped plane curve formed by a point on the circumference of a circle rolling around another equal circle. Its standard polar equation gives a clear example of a radius varying with angle.

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