>>In some non-Euclidean geometries...
>
>Would that be like Hunter Thompson's geometry?

No, but in both hyperbolic (classical Reimannian) and spherical geometries, all lines are curved (both are 4 postualte geomteries that specifiy that given a line and a point not on that line, there exist either many (hyperbolic) or no (spherical) lines parallel to the given line passing through the point, and so the sum of the angles of a triangle in these geometries will not be pi/2), and in taxicab geometries, all lines not on a common axis contain at least one 90 degree angle movement.