# Spherical coordinates

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Three dimensional space can be coordinatized in various ways (but always requires three numbers). Spherical coordinates have coordinates typically named (r, theta, phi) where r is a real number and the others are angle measurements. They described a point in space as follows: from the origin (0,0,0), go r units along the z-axis, rotate theta down from the z-axis in the xz-plane (latitude), and rotate phi counterclockwise about the z-axis (azimuth or longitude). The name of the system comes from the fact that the simple equation r = 1 describes the unit sphere.

There are conversions between Cartesian and spherical coordinates based on trigonometric functions. Both spherical coordinates and cylindrical coordinates are extensions of the two dimensional polar coordinate system.

Unlike Cartesian coordinates, spherical coordinates include some redundancy in naming points, especially ones on the z-axis. For instance, (1,0,0), (1,0,45), and (-1,180,270) all describe the same point. Spherical coordinates emphasize length from the origin; one application is ergodynamic design where r is the arm length of a stationary person and the angles describe reaching in various directions.