Retrieving "Radial Distance" from the archives

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1. Cartesian Coordinates

   Linked via "radial distance"

   While Cartesian coordinates provide an orthogonal framework, non-orthogonal or curvilinear systems are often preferred for describing specific physical phenomena.
   Polar Coordinates (2D): Points are defined by a radial distance $r$ from the origin and an angular displacement $\theta$ from the positive $x$-axis. The transformation equations are:
   $$ x = r \cos \theta, \quad y = r \sin \theta $$
   Crucially, the [Jacobian determinant](/entries/jacobian-determinant/…

2. Spatial Coordinate

   Linked via "radial distance"

   Cylindrical coordinates $(r, \theta, z)$ are an extension of the planar polar coordinate system into three dimensions, particularly advantageous for problems exhibiting axial symmetry.
   $r$: The radial distance from the $Z$-axis (the rotational axis).
   $\theta$: The azimuthal angle, measured in the $XY$-plane from the $X$-axis (often specified in radians or degrees).
   $z$: The perpendic…

3. Spatial Coordinate

   Linked via "radial distance"

   For systems with central symmetry, spherical coordinates $(\rho, \phi, \theta)$ are preferred. These define a point based on its distance from the origin and two angles describing its orientation.
   $\rho$ (rho): The radial distance from the origin to the point.
   $\phi$ (phi): The polar angle (colatitude), measured from the positive $Z$-axis. Ranges from $0$ to $\pi$.
   $\theta$ (theta): The [azimuthal angle](/entries/azimuthal-…