GEOMETERS are wont to speak (it seems to me) somewhat laxly of “the line at infinity” as if there were only one such line in a plane; in a certain but not in the most obvious sense this is true—viz.

Important update, Jan. 17 at 18:00 UTC: There have been a lot of objections raised about the video mentioned below and the way I describe the math therein. It’s more than I can simply add or update ...