My name is Alexander FufaeV and here I write about:
Polar Coordinates: How to Simplify 2D Problems with Circular Symmetry
Polar coordinates are a set of two coordinates that describe the position of a point in the plane. In contrast to the usual Cartesian coordinates \( (x,y)\), polar coordinates \((r, \varphi)\) indicate a point on an imaginary circular plane.
$$ \begin{align} \begin{bmatrix} x \\ y \end{bmatrix}~=~ \class{red}{r} \begin{bmatrix} \cos(\class{green}{\varphi}) \\ \sin(\class{green}{\varphi}) \end{bmatrix} \end{align} $$