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Reference.org
Spherical coordinate system
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a spherical coordinate system specifies a given point in <a href="/facts/Three-dimensional_space/KAqKWUbS">three-dimensional space</a> by using a distance and two angles as its three <a href="/facts/Coordinate_system/Mtd0q4SP">coordinates</a>. These are </p> <ul><li>the radial distance r along the line connecting the point to a fixed point called the <a href="/facts/Origin_(mathematics)/Lm26tRCB">origin</a>;</li> <li>the polar angle θ between this radial line and a given <i>polar axis</i>; and</li> <li>the azimuthal angle φ, which is the <a href="/facts/Angle_of_rotation/a4VjkXGe">angle of rotation</a> of the radial line around the polar axis.</li></ul> <p>(See graphic regarding the "physics convention".) </p><p>Once the radius is fixed, the three coordinates (<i>r</i>, <i>θ</i>, <i>φ</i>), known as a 3-<a href="/facts/Tuple/BI1HIxL8">tuple</a>, provide a coordinate system on a <a href="/facts/Sphere/jywYLNM2">sphere</a>, typically called the spherical polar coordinates. The <a href="/facts/Plane_(geometry)/tAUtRFcn">plane</a> passing through the origin and <a href="/facts/Perpendicular/u0k8xqx4">perpendicular</a> to the polar axis (where the polar angle is a <a href="/facts/Right_angle/psaslRq7">right angle</a>) is called the <i>reference plane</i> (sometimes <i><a href="/facts/Fundamental_plane_(spherical_coordinates)/n5cWNMq2">fundamental plane</a></i>). </p>