Quote Originally Posted by zaza
However, what happens if you roll the paper into a cylinder so that the two ends of the line meet? Do you have a line or a circle? In that instance, the dimension in which the curvature acts is not the same as that in which the line acts. This is different from drawing a circle on the paper using a compass. General relativity....
Interesting but misleading I think. By rolling up the paper you are effectively changing the axis along which the centre-point of the circle is found.

Lets say you draw the line near the top of the A4 page, the centrepoint would be down the page (and keep going forever in that direction). BUT if you roll up the paper while still on the desk then the centrepoint will be vertically (a couple of inches) above the desk. So you have altered the circle's plane by 90 degrees (around the X axis).

The new radius would not be comparable because the original line now occupies 3 dimensions (drum-roll please...). The original line (now curved back on itself) would actually lie along the surface of an infinitely large SPHERE!! The centre of this sphere would also be a couple of inches above the desk BUT INFINITELY far down the page.

OMG I surprise myself sometimes.

I hope this makes sense to someone.