Is that really true? I mean the radius of the fold is going to mean the outside most layer is going to have to get larger and larger relative to the inner most

Is that really true? I mean the radius of the fold is going to mean the outside most layer is going to have to get larger and larger relative to the inner most layer. If it's 1 mile thick then the outer layer will need to be 3.14 miles longer than the inner layer. Won't that have some kind of effect? Is it all proportional or will the length of that difference eventually make it so the outer piece can't stretch/bend/flex over that great a distance (in reality vs magically friction-less paper)