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    Spherical Coordinates

    Illustration

    Illustration

    Alternate names

    spherical coordinate system | spherical polar coordinates

    Basic definition

    Spherical coordinates are a coordinate system in which points in three-dimensional space are given by two angles and a distance from the origin.

    Detailed definition

    Spherical coordinates, also called spherical polar coordinates, are a system of curvilinear coordinates that are natural for describing positions on a sphere or spheroid. Define θ to be the azimuthal angle in the x y-plane from the x-axis with 0<=θ<2π (denoted λ when referred to as the longitude), ϕ to be the polar angle (also known as the zenith angle and colatitude, with ϕ = 90° - δ where δ is the latitude) from the positive z-axis with 0<=ϕ<=π, and r to be distance (radius) from a point to the origin. This is the convention commonly used in mathematics.

    Related terms

    azimuth | colatitude | great circle | latitude | longitude | oblate spheroidal coordinates | polar angle | polar coordinates | polar plot | polar vector | prolate spheroidal coordinates | zenith angle

    Related Wolfram Language symbol

    SphericalPlot3D

    Educational grade level

    high school level

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