The Bekenstein–Hawking entropy is defined by the relation
$$S=\frac{k_BA}{4l_p^2},$$
where $k_B$ is the Boltzmann constant and $A$ is the area of the black hole's event horizon in units of the Planck area $l^2_p$.
I am not familiar with black holes thermodynamics, so I have three relatively simple questions.
Where does the proportionality constant $\frac{1}{4}$ come from and how do you interpret it?
I tried to find a clear answer but always get confused.If you consider the black hole as a 2D disc or circle (not a 3D sphere). Would I have the same expression (in the same unit) and in particular, the same proportionality constant ?
In the derivation of the formulae, is there any assumption on the shape of the black hole ? For instance that it is a sphere or whatever the shape.