The shape of multidimensional gravity
  In the case of one extra dimension, well known Newton's potential $\phi
(r_3)=-G_N m/r_3$ is generalized to compact and elegant formula
$\phi(r_3,\xi)=-(G_N m/r_3)\sinh(2\pi r_3/a)[\cosh(2\pi
r_3/a)-\cos(2\pi\xi/a)]^{-1}$ if four-dimensional space has topology
$\mathbb{R}^3\times T$. Here, $r_3$ is magnitude of three-dimensional radius
vector, $\xi$ is extra dimension and $a$ is a period of a torus $T$. This
formula is valid for full range of variables $r_3 \in [0,+\infty)$ and $\xi\in
[0,a]$ and has known asymptotic behavior: $\phi \sim 1/r_3$ for $r_3>>a$ and
$\phi \sim 1/r_4^2$ for $r_4=\sqrt{r_3^2+\xi^2}<<a$. Obtained formula is
applied to an infinitesimally thin shell, a shell, a sphere and two spheres to
show deviations from the newtonian expressions. Usually, these corrections are
very small to observe at experiments. Nevertheless, in the case of spatial
topology $\mathbb{R}^3\times T^{d}$, experimental data can provide us with a
limitation on maximal number of extra dimensions.
