To get a step deeper into your “how can a machine draw a circle” question. Mostly it can’t. Even with an open-loop control system dragging the ‘pen’ at a fixed angle, you would need to have defined that curve in software somewhere, where it will be a barely-noticable set of X-Y steps, not a pure curve, otherwise you cannot be sure it would return to the origin.

Luckily, you only need a few decimals of pi to approximate that far beyond what any human eye could discern.

Break any digitally defined curve down far enough and you will see those discrete steps, but with modern technology, we just never notice it.