Editing Spherical coordinate system (section)

==Terminology==
{{hatnote|The physics convention is followed in this article; (See both graphics re "physics convention" and re "mathematics convention".)}}

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 vector|normal angle]]'', or the ''[[colatitude]]''. The user may choose to replace the inclination angle by its [[angular complement|complement]], the ''[[elevation angle]]'' (or ''[[altitude angle]]''), measured upward between the reference plane and the radial line{{mdash}}i.e., from the reference plane upward (towards to the positive z-axis) to the radial line. The ''depression angle'' is the negative of the elevation angle. ''(See graphic re the "physics convention"{{mdash}}not "mathematics convention".)''

Both the use of symbols and the naming order of tuple coordinates differ among the several sources and disciplines. This article will use the ISO convention<ref>{{Cite web |title=ISO 80000-2:2019 Quantities and units – Part 2: Mathematics |url=https://www.iso.org/standard/64973.html |access-date=2020-08-12 |website=ISO |date=19 May 2020 |pages=20–21 |language=en |id=Item no. 2-17.3}}</ref> frequently encountered in ''physics'', where the naming tuple gives the order as: radial distance, polar angle, azimuthal angle, or ''<math>(r,\theta,\varphi)</math>''. (See graphic re the "physics convention".) In contrast, the conventions in many mathematics books and texts give the naming order differently as: radial distance, "azimuthal angle", "polar angle", and <math>(\rho,\theta,\varphi)</math> or <math>(r,\theta,\varphi)</math>{{mdash}}which switches the uses and meanings of symbols θ and φ. Other conventions may also be used, such as ''r'' for a radius from the ''z-''axis that is not from the point of origin. Particular care must be taken to check the meaning of the symbols. <!-- Please maintain a consistent convention in this article. -->

[[File:3D Spherical 2.svg|thumb|The '''''mathematics convention'''''. Spherical coordinates {{math|(''r'', ''θ'', ''φ'')}} as typically used: radial distance {{mvar|r}}, azimuthal angle {{mvar|θ}}, and polar angle {{mvar|φ}}. + ''The meanings of {{mvar|θ}} and {{mvar|φ}} have been swapped''{{mdash}}compared to the '''physics convention'''. The 'south'-direction x-axis is depicted but the 'north'-direction x-axis is not. (As in physics, {{mvar|ρ}} ([[rho]]) is often used instead of {{mvar|r}} to avoid confusion with the value {{mvar|r}} in cylindrical and 2D polar coordinates.)]]

According to the conventions of [[geographical coordinate system|geographical coordinate systems]], positions are measured by latitude, longitude, and height (altitude). There are a number of [[celestial coordinate system]]s based on different [[Fundamental plane (spherical coordinates)|fundamental planes]] and with different terms for the various coordinates. The spherical coordinate systems used in mathematics normally use [[radian]]s rather than [[degree (angle)|degrees]]; (note 90 degrees equals {{fraction|π|2}} radians). And these systems of the  ''mathematics convention'' may measure the azimuthal angle ''counterclockwise'' (i.e., from the south direction {{mvar|x}}-axis, or 180°, towards the east direction {{mvar|y}}-axis, or +90°){{mdash}}rather than measure ''clockwise'' (i.e., from the north direction x-axis, or 0°, towards the east direction y-axis, or +90°), as done in the [[horizontal coordinate system]].<ref>Duffett-Smith, P and Zwart, J, p. 34.</ref> ''(See graphic re "mathematics convention".)''

The spherical coordinate system of the ''physics convention'' can be seen as a generalization of the [[polar coordinate system]] in [[three-dimensional space]]. 
It can be further extended to higher-dimensional spaces, and is then referred to as a [[N-sphere#Spherical coordinates|''hyperspherical coordinate system'']].