Is there really such a thing as a perfect circle in nature?

[Danger]

If we neglect the drag of air that deforms the drop, and many other small effects.

Still not in the ballpark. There are definite molecular and atomic "bumps" in the surface.

 

[krononauten]

Well I think things like electric field lines are circular.

That depends on the antenna structure.
Magnetic field lines are circular around a perfect conductor carring a constant current as given in the classic example.

 

[Dr Lots-o'watts]

I don't see how error is relevant to a definition. We define things arbitrarily, and usually exactly.

That's mathematics, the tools in our minds.

Error comes in when we measure and model.

That's physics, the things we measure in nature.

The link between the two : the models that take error into account (such as HUP for the small scale.)

Of course the word "perfect" pretty much excludes anything. Even black holes can't be perfect because there is always something falling in it that breaks the symmetry (or quantum radiation coming out).

 

[robindude]

Suppose there was a perfect circle in nature.

We can measure this to some amount, suppose 14 decimal places (or a thousand, or a googol, whatever you like, I'll use 14 for sake of argument).

We check a possible perfect circle that really IS perfect, to infinite decimal places. We confirm this when our measurements cannot find any flaw.

We check a possible perfect circle that is NOT perfect, but has an error that is smaller than our ability to detect. The circle still appears perfect.

Result: It doesn't matter if there IS a perfect circle in nature or not, we have no way of determining the validity of its existence as perfect, merely as 'perfect to the limit of our ability to measure'.

Just an opinion. Probably not helpful.