Re: [math-fun] Curved space paradox

On 19/02/2018 19:30, Allan Wechsler wrote:

The following intuitive line of reasoning leads to a contradictory conclusion, and I don't know what's wrong with it. Obviously one of my assumptions or beliefs about spaces with constant Gaussian curvature is wrong, but I can't figure out which.

The bit where I immediately felt "uh-oh, handwaving going on here, not at all convinced" was this:

But as r gets larger, the negative curvature of the ambient hyperbolic space begins to make itself felt, and the circumference goes above 2 pi r, by some factor related to sinh.

I don't see why this should be true. -- g