[Giho]

I don't understand how they do the comparison between the torus and sphere. First to take a rectangular paper as an example for a torus and then say some parts would stretch doesn't make a scientific comparison to a sphere. As I understand the only difference between a sphere and a torus geometrical is that as a flat piece the sharp tops are cut of a flat piece of sphere. See link for picture of flat sphere: https://www.cadforum.cz/img/petals.gif

[somewhereoutth]

One way to see the difference is to consider a loop on the sphere or torus. On a sphere, any loop can always be drawn tighter until it is a point. On a torus, there will be some loops that cannot be drawn tight, as they go 'through the hole'. Another way is to imagine the sphere and the torus are hairy. You can comb a torus such that all hairs lie in more or less the same direction as their neighbours - if you try this with a sphere, there will be at least one point where the hairs completely diverge.