In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three real numbers: the radial distance r along the radial line … See more

To define a spherical coordinate system, one must designate an origin point in space, O, and two orthogonal directions: the zenith reference direction and the azimuth reference … See more

It is also possible to deal with ellipsoids in Cartesian coordinates by using a modified version of the spherical coordinates.
Let P be an ellipsoid specified by the level set
$${\displaystyle ax^{2}+by^{2}+cz^{2}=d.}$$
The modified … See more

The radial distance from the fixed point of origin is also called the radius, or radial line, or radial coordinate. The polar angle may be called inclination angle, zenith angle, normal angle, or the colatitude. The user may choose to ignore the inclination angle and use the … See more

Just as the two-dimensional Cartesian coordinate system is useful—has a wide set of applications—on a planar surface, a two-dimensional … See more

As the spherical coordinate system is only one of many three-dimensional coordinate systems, there exist equations for converting coordinates between the spherical coordinate system and others.
Cartesian coordinates
The spherical … See more

The following equations (Iyanaga 1977) assume that the colatitude θ is the inclination from the positive z axis, as in the physics convention discussed.
The line element for an infinitesimal displacement from (r, θ, φ) to (r + dr, θ + dθ, φ + dφ) is See more