Main Question or Discussion Point
What's the circumference of a circle of radius r, on a sphere of radius R?
The following i the context I was talking about:The circumference of a circle of radius r is [itex]2\pi r[/itex], whether it is on a sphere or not.
If r == PI*R, the circumference created by the string will be zero.Imagine you fix one end of a string with the length r at a point in 2d-space, and make a full circle with the other end. If you then find that the circumference of that circle is different from 2*PI*r, you conclude that the 2d-space is curved intrinsically.