n}}})/b_0$ where $b_0$ is the Einstein radius of an SIS with velocity dispersion $\sigma_v$, as well as the projected axis ratio $q({{\mathbf{\hat n}}})$, for an isothermal ellipsoid with axis ratios $q_1=0.75,\  q_2=0.5$. We can see the Einstein radius of the projected profile is maximized when projecting along the long axis of the halo, whereas the ellipticity is maximized when projecting along the middle axis of the halo, as it should be. Note we have only considered the range $\theta\in[0,\pi/2]$ and $\phi\in[0,\pi/2]$ rather than the full range of possible lines of sight $\theta\in[0,\pi/2]$ and $\phi\in[0,2\pi]$. This is due to the symmetry of our model; all eight of the octants defined by the symmetry planes of the ellipsoids are identical.

Let us now go back and study the distribution of line of sights for both doubles and quads. Figure \[fig:losdist\] shows these distributions for three types of halos: a prolate halo, an oblate halo, and a halo that is neither strongly oblate nor strongly prolate. As is customary, we parameterize the halo shape in terms of the shape parameter $T$ which is defined as $$T = \frac{1-q_1^2}{1-q_2^2}.
\label{eq:shape_parameter}$$ Note that a perfectly prolate halo ($q_1=q_2$) has $T=1$, whereas a perfectly oblate halo 