But then you could take that vicious circle and twist it just so and end up with a vicious ball, which may then crack, bringing us full circle.
You can't transform a circle into a sphere because of the hole.
That is one cracked ball. But not mine.
Break the vicious circle, Graphitone; the 2d equivalent, as Care suggests (& John refutes, TBH) of cracking a ball. Do it.
Not John refuting. The magic of topology refutes. If only I could take the credit for the refutage!
No, it's no good. Please explain what you're on about. Whatever shaped ball you want to bring up, you can't get there from a circle because a circle has a hole through it.