What is Stereographic projection, equal-angle net, equal-area projection, pole?

Let a line through the centre $O$ of a sphere of radius $R$ meet the lower hemisphere at $P$, at the angle $\theta = 90{}^{\circ} - p$ from the nadir, where $p$ is the plunge of the line and $t$ its trend. The stereographic projection maps $P$ to the point where the straight line from the zenith to $P$ crosses the horizontal plane through $O$; that point lies at the distance $r$ from $O$ in the azimuth $t$. The chart of the lower hemisphere drawn this way, with its grid of great and small circles, is the equal-angle net (or Wulff net). The equal-area projection (of the sphere) maps $P$ to the point at the distance $r = R\sqrt2\sin(\theta/2)$ in the azimuth $t$; its net is the Schmidt net. The pole of a plane is its normal line, plotted as a point: for a plane of dip direction $\alpha$ and dip $\delta$, the pole trends $\alpha + 180{}^{\circ}$ and plunges $90{}^{\circ} - \delta$.