For randomly oriented rods, Pike and Seager using a MC simulation obtained $n_cl^2\simeq 5.71$ [@Pike1974]. Subsequently, for $n_cl^2$, the following values have been obtained $5.615$ [@Balberg1983], $5.63$ [@Dalafi2010], $ 5.6372858(6)$ [@Mertens2012], $5.754$ [@Mietta2014] and $5.63726\pm 0.00002$ [@Li2009]. The total excluded area for this problem can be estimated as $V_{ex}^t=n_cV_{ex}=(2/\pi)n_c l^2\approx 0.64n_c l^2$.

The more general case of an anisotropic system of rods has also been analyzed [@Balberg1983; @Balberg1983a; @Balberg1984]. The rods were aligned with respect to a selected direction, $x$. Their axes were randomly distributed within some interval such that, $-\theta_m \leq \theta\leq \theta_m$, where $\theta_m\leq \pi/2$. The isotropic case is given by $\theta_m=\pi/2$, and the smaller the $\theta_m$ the higher the degree of orientation. The macroscopic anisotropy of the system was characterized by the value $$\label{eq:Anisotropy}
A = \langle |\cos\theta| \rangle/\langle |\sin\theta| \rangle = \sin \theta_m/(1-\cos \theta_m).$$ Here and below $A=P_{\parallel}/P_{\perp}$ to simplify notation. For the isotropic case, $A=1$, whereas for the highly anisotropic case ($\theta_m\rightarrow 0$), $A\rightarrow \infty$ [@Pike1974; @Balberg1982a].

The percolation threshold for this system increases with the macroscopic anisotropy $A$ [@Balberg1983a; @Balberg1984a]. The dependence of the percolation number density on the degree of macroscopic anisotropy was approximated as $$\label{eq:NumberDensityAnisotropy}
n_c^*=n_c/n_c^i=0.5(A + A^{-1}),$$ where $n_c^i$ is the 