
Yes, that is exactly how I came to that algorithm. I had been trying to create a solid ring. At one point in desperation I started with the same polygon approach you tried, but I stopped when I hit the point limit.
It isn't described on the English wikipedia, I don't think I saw it on the German one either even though it lists many more circle drawing algorithms than the English one.
I haven't been able to read the original paper by Andres, it is paywalled, but I have read some of his later papers* and others that expand on the work. If you want to see the proof (or just out of interest) they can be found online.
 I say read, but I don't understand most of it. It took me a long time before I even remembered how the notation for sets worked.
 I say read, but I don't understand most of it. It took me a long time before I even remembered how the notation for sets worked.
this looks as if you would draw concentric rings with an increasing radius. How can you prove, that discretisation does not produce small "holes" in your ring?
Addendum: I'm currently reading the french Wikipedia entry (well, after translation into german  my french is not good enough for maths) and it seems to be a characteristic of that algorithm that no holes are left