demoivre

The genus, apparently, of a curve in Real two-space is built from the Complex geometry of a sphere (genus zero) to a torus (genus one) to a two-holed torus (genus two) to an n-holed torus (genus n). If you bisect any one of these shapes with a Real plane, you get the shape of a two dimensional curve mapped onto the plane by the Complex shape (either the sphere or the n-torus). Real-plane curves are linked to their genera via a formula that involves their degrees--as such, all conics (ellipses, parabolas, hyperbolas, etc) have genus zero. So do lines.

Genus zero means that all lines and conics are generated by spheres and can be viewed as effectively indistinguishable from each other.

Red mathematician needs sleep badly....