In article <email@example.com>, Leon Aigret <firstname.lastname@example.org> wrote:
> The line segment from (0, 0) to (1, 1/2) fits because -- with the > whole square shaped region divided into nine subsquares -- it avoids > the central subsquare and in the subsquares through which it does > pass, the position of the intersection is similar to the position of > the whole line segment in the whole region. > > Similarly, the line from (0, 1/2) to (1/2, 0) is an example for the 45 > degrees orientation.
So, these are solutions to the original question! To see that they work does not require the omitted "tedious details". (Those details are used to show that no other slopes are possible.)