Conic sections and the regulus

Well, you know conic sections take a plain
right cone, and various sections of it result
circles, ellipses, parabolas, and hyperbolas.

The idea is that the cone is an example
of a regulus, which is a three-dimensional
space surface, that is all drawn with lines,
as what intersect and cross, so to result
a regulus.

A plane, for example, is a simplest sort of
regulus, for example that it's a set of points,
and that all the lines on the plane, draw it,
vis-a-vis, only left-right lines like scan-lines,
or that there's left-right and up-down lines,
or any sort of way you can imagine lines,
in a line, that result a plane.

The right cone, it's a regulus, it's like uncooked
spaghetti, or stalks of what and making a sheaf,
all the lines through the point of the cone,
thus it results a double-cone, the regulus.

The swept hyperbola, it's also a regulus, about
that the regulus, results either like a plane or
like a cone, about the orthogonal coordinates,
and the polar coordinates. So DesCartes gives
coordinates, for example, while these regulus
components, then have transforms what make
for the same kind of thing in a different way.

So, conic sections are very well explored, then
for getting into the regulus, about that it makes
regular forms in a medium-dimensional surface
in higher dimensions, made from lower dimensions,
here sort of just like how points make lines, or
point-sets and the whole modern apparatus,
then how lines make the plane-regulus, the
cone-regulus, the hyperbola-regulus, and otherwise
getting into surfaces that are or aren't representable
as a regulus, then for the fixed-points and singularities
as multiplicities of those, about the affine and the
perspective and projective, vis-a-vis, geometry.

https://en.wikipedia.org/wiki/Regulus_(geometry)
https://en.wikipedia.org/wiki/Translation_plane#Reguli_and_regular_spreads
https://en.wikipedia.org/wiki/Conic_section