Why do the avenue lines meet at an antipode? In Manhattan, they are parallel, they don't converge.
I understand the difference between latitude and longitude lines. A meridian of longitude is a great circle centered at the Earth's center; a line of latitude is a small circle (the analogue of a chord in a 2D circle on a plane) whose center lies north or south of the Earth's center in three dimensions. Longitude lines divide a sphere like slices of an orange, converging at poles; latitude lines divide a sphere like a tomato slicer and do not converge.
There's actually two "poles"; aside from the one in Uzbekistan that everyone is seeing, there's another in the South Pacific Ocean at the antipodal point from Uzbekistan. So the avenues are being treated as meridian lines; great circles. Would it be more accurate to extrapolate avenues as parallel small circles?
We could test this theory by inspecting whether Manhattan's actual grid respects the curvature of the Earth. If the avenues are closer together at the northern end of the island, then the avenues actually do behave as meridians. If not, then the extrapolated avenue lines should be small circles and would not converge. You'd still have a pole in Uzbekistan, where the last street becomes an arbitrarily small circle, but just one avenue line through it. (I gotta run at the moment but will throw some trigonometry at this later.)