Browse Definitions :

polar coordinates

Polar coordinates provide a method of rendering graphs and indicating the positions of points on a two-dimensional (2D) surface. The polar coordinate system is employed in mathematics, physics, engineering, navigation, robotics, and other sciences.

The polar plane consists of a reference axis, or ray, that emanates from a point called the origin. Positions or coordinates are determined according to the distance or radius, from the origin, symbolized r , and the angle relative to the reference axis, symbolized by the lowercase Greek theta ( ). In the most common polar system, the reference ray points off toward the right, and angles are measured counterclockwise from it (illustration at left). This scheme is preferred, and is used by mathematicians, physicists, and engineers. In a less common scheme, the reference ray points upward, and angles are measured clockwise from it (illustration at right). This method is sometimes used by astronomers, navigators, military personnel, meteorologists, and robotics engineers.

Points or coordinates in either system are indicated by writing an opening parenthesis, the r value, a comma, the value, and a closing parenthisis in that order. The radius coordinates are, by convention, always nonnegative. Angles can be specified in degree s from 0 to 360, or in radian s from 0 to 2 pi , where pi is approximately 3.14159. An example using degrees is ( r , ) = (2,30). The origin is assigned r = 0.

If the scheme in the left-hand illustration is used, it is possible to convert a coordinate in the Cartesian xy -plane to polar values using these formulas:

x = r cos

y = r sin

Conversely, to convert a coordinate in the polar plane (as depicted in the left-hand illustration) to Cartesian values, use these formulas:

r = ( x 2 + y 2 ) 1/2

= arctan ( y / x )

Compare Cartesian coordinates .

This was last updated in September 2005



  • cyber attack

    A cyber attack is any attempt to gain unauthorized access to a computer, computing system or computer network with the intent to ...

  • backdoor (computing)

    A backdoor is a means to access a computer system or encrypted data that bypasses the system's customary security mechanisms.

  • post-quantum cryptography

    Post-quantum cryptography, also called quantum encryption, is the development of cryptographic systems for classical computers ...



  • risk mitigation

    Risk mitigation is a strategy to prepare for and lessen the effects of threats faced by a business.

  • call tree

    A call tree is a layered hierarchical communication model that is used to notify specific individuals of an event and coordinate ...

  • Disaster Recovery as a Service (DRaaS)

    Disaster recovery as a service (DRaaS) is the replication and hosting of physical or virtual servers by a third party to provide ...


  • cloud SLA (cloud service-level agreement)

    A cloud SLA (cloud service-level agreement) is an agreement between a cloud service provider and a customer that ensures a ...

  • NOR flash memory

    NOR flash memory is one of two types of non-volatile storage technologies.

  • RAM (Random Access Memory)

    RAM (Random Access Memory) is the hardware in a computing device where the operating system (OS), application programs and data ...