Non-Parallel

The east end of the Times Square subway station, where the shuttle meets the concourse leading to the Seventh Avenue trains:

This spot is one of the last remaining pieces of the original 1904 station, including the cast iron columns, the curved shuttle track, and the tile and brick wall on the right. Before the system expansion that converted the east-west segment of the original line to the shuttle, and converted the northern half of the original line, on Broadway above 42nd Street, to the northern half of the Seventh Avenue line, this station was on a curve as the tracks switched from generally north-south under Broadway to east-west under 42nd Street. That curve actually passes through part of the subgrade structure of the old New York Times building on the tiny triangular block between Seventh, Broadway, and 42nd.

So there are three geometries here: the rectangular grid represented by Seventh and 42nd, the meandering diagonal line of Broadway, and the smooth curve of the tracks connecting the two. The wall on the right is, I believe, parallel to the line of 42nd; and the tracks are curving off to the left, up to the north.