A SIMPLE CHALLENGE that you great Mathematicians won't answer...

Consider a circle: x^2 + y^2 = c

To construct a 'perfect mathematical circle'
requires delta x and delta y to BE zero
from point-to-point in the circle -
not just 'approach zero'.

If delta x and delta y have ANY magnitude
from point-to-point then the 'circle' is a polygon.
It is irrelevant as to how many sides the polygon has -
it could be a billion^billion facets
but it will still be a polygon.

If delta x and delta y are allowed to be zero
from point-to-point in the 'circle'
then we are discussing one point only - not a circle.

How do you try to explain this obvious situation????
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