My name is Alexander FufaeV and here I write about:
Spherical Coordinates: How to Solve Problems with Spherical Symmetry
Spherical coordinates are a set of three coordinates that describe the position of a point in three-dimensional space. In contrast to the more common Cartesian coordinates \((x,y,z)\), the spherical coordinates \((r,\theta,\varphi)\) indicate a point on a sphere. Both coordinate systems are equivalent, but use different symmetries. In the case of spherical coordinates, spherical symmetry of a problem is utilized:
$$ \begin{align} \begin{bmatrix} x\\y\\z \end{bmatrix}~=~\class{red}{r}\begin{bmatrix} \sin(\class{blue}{\theta})\,\cos(\class{green}{\varphi})\\\sin(\class{blue}{\theta})\,\sin(\class{green}{\varphi})\\\cos(\class{blue}{\theta})\end{bmatrix} \end{align} $$