> So you're saying, that an inhabitant of a toroid or > cylinder - on its 2-D surface - cannot draw any shape > which will tell them it's warped? I find that hard to swallow.
If he could go around the cylinder (leaving a mark at his starting point) he'd see it's closed .If the cylinder were big enough, he would think he's living in an infinite flat space. However, closure is a global property. Curvature is a local property. He still wouldn't be able to tell if he's in a round cylinder , an oval cylinder, a "flattened cylinder" , an infinitely long parallelepiped http://ars.els-cdn.com/content/image/1-s2.0-S0021999104001500-gr1.jpg , etc .