Date: Jul 25, 2013 9:47 AM
Author: Narasimham
Subject: Asymptotic lines of a polar grid

Please refer to my earlier discussion on (imaginary) asymptotic lines for positive gauss curvature surfaces.
(My name does not appear here!. Can Mathforum help for its full access?)

Stretching it further and looking at these "asymptotic" lines as limiting cases for very small flat curvatures,
polar grid (r,theta), becomes ( (r + theta)/2, ( r - theta)/2 ) archimedian spirals.

It puzzles me that the particular two dimensional case of spirals are not any special lines in elliptic or hyperbolic geometry.