Fun question one: can anyone see the relation between the following three figures? Note: I made a (sort of subtle) mistake in one of them….the one where the graph lines are showing)
Fun question two (a bit harder):
What is the relation between these figures?
And for the win: what is going on here? (this is ambiguous)
Ok, I’ll help you with the last one: imagine this process (one solid torus (think: doughnut or bagel) inside a larger one, and repeat this process (think: those Russian dolls that are nested). If you then take the infinite intersection, you get a simple closed curve (not obvious) that is so badly embedded, it fails to pierce a disk at any of its points (and certainly fails to have a tangent vector anywhere).