As you already know, the interior of a circle is represented by an inequality. For example,
for the unit circle. Today I was thinking by myself and I wondered if there is a curve that could represent every point inside of a circle. Maybe with a spiral like this,
If you can't represent it perfectly with a curve, what would be the closest way to represent it?
This question is asked merely out of curiosity, it may be completely irrelevant or meaningless :)