Sleepless musings, part 2
Yeah, I can't sleep again. *grumbles at flu* *hacks up a lung*
Here's tonight's random sleepless idea: what sorts of crazy shenanigans could one pull with a concave rope?
What do I mean by a concave rope? Well, imagine a regular rope. If you wrap it around a convex surface, like a closed box, or a potato, and tighten it, it'll tightly hug the whole surface. But if you wrap it around a concave surface, and the rope goes over the concave bit, it'll skip some of the surface. For instance, if you wrap the rope around a coffee mug from top to bottom, so it goes over the opening of the mug, it'll go across the top of the mug, through midair, when you pull it tight. It's not going to go down the inside of the mug to the bottom, across, and back up.
But... what if you had a rope that *did* do that? What sorts of crazy stuff could you do? Or, better yet, what if you had concave plastic wrap?
(Also, I just made up the term "concave rope" off the top of my head. Does anyone know of a mathematically/topologically proper name for this?)
Here's tonight's random sleepless idea: what sorts of crazy shenanigans could one pull with a concave rope?
What do I mean by a concave rope? Well, imagine a regular rope. If you wrap it around a convex surface, like a closed box, or a potato, and tighten it, it'll tightly hug the whole surface. But if you wrap it around a concave surface, and the rope goes over the concave bit, it'll skip some of the surface. For instance, if you wrap the rope around a coffee mug from top to bottom, so it goes over the opening of the mug, it'll go across the top of the mug, through midair, when you pull it tight. It's not going to go down the inside of the mug to the bottom, across, and back up.
But... what if you had a rope that *did* do that? What sorts of crazy stuff could you do? Or, better yet, what if you had concave plastic wrap?
(Also, I just made up the term "concave rope" off the top of my head. Does anyone know of a mathematically/topologically proper name for this?)