I don't think my work knows what telnet is, so I don't think there is problem. My bosses main concern is personal abuse of computer time during work hours. Some of the office email their family back and forth a lot...
Anyway, I discovered polars in a small book on algebra (Littlewood). The point to book was to give examples of math that acted like skeleton key, opening many door with a single key. That's what playing around with polars will do.
It's hard to explain but actually drawing out a polar to a point with respect to a circle, or constructing the figure the other way, given a polar, find the point or set of points. For me, because of the way my mind works, this figure opened up the entire world of invariants and transformations. Technically this is a linear inversion transformation of the complex plane onto itself.
The deeper you go into polars the more and more you find. It is also the reflections on the surface of a cone, seen from the point of the cone (as the center of the circle). In these conic reflections of figures on the perpendicular plane, lines are transformed to circles, circles go to circles, and asymetric shapes are inverted.
Polar lines and points can also be found for all the conic sections, and their surfaces of revolution. What I think is going, is polars are set of lines that also include tangents and diameters as a special case.
The full linear group has four subgroups (cyclomic theory of equations), in which the algebraic form of polars is one member (1/z) where z is a complex. The others are:
1. az
2. az + b
3. 1/z
4. az - b/cz - d
One and two are euclidean transformations (rotations, translations of the plane onto itself), three are conic, hyperbolic, parabolic inversions, and four is projective (spherical).
Now why would I want to know this stuff? Because it opens the doors to the math used in mathematical physics, so you can see what they are doing, and how they have put together models of the universe. And most important (I think) it is a highly technical, but nevertheless a form of metaphysics. These are part of the fundamental ideas physical science uses. They compose a kind of ontology of space-time.
I didn't get all that from polars, of course. The symetries of the square were another magic math toy.
(Caution. Some of this is going to be wrong. I am typing this in the wheelchair shop, working on a build, and I have a hang over...)
C