Planck Length Paradox: Radius & Area

[Shootertrex]

Assuming that a Planck length is the smallest unit of distance, I propose this:

Assume there was a circle of radius r and had an area of A. If I would increase this circle's area by 1 Planck length^2, would the radius change? The radius would theoretically change by less than a Planck length, but would the radius actually change?

Another would be if I increased this circle's diameter by 1 Planck length. Would the radius increase?

Are these true paradoxes, something that just happens at this level or do they not hold any water?

 

[phlip180]

I am certainly not an expert in Planck measurements (and I really doubt there is such a thing as a Planck expert), but I'm fairly certain there are 2 different measurements called Planck Length and Planck Area. Planck Area is a smaller unit than Planck length for the exact reason you are bringing up. There is also Planck Volume and I believe other similar measurements for higher dimensions, though I'm not sure how many of these have an established value as of yet.

 

[mathman]

Assuming that a Planck length is the smallest unit of distance, I propose this:

Assume there was a circle of radius r and had an area of A. If I would increase this circle's area by 1 Planck length^2, would the radius change? The radius would theoretically change by less than a Planck length, but would the radius actually change?

Another would be if I increased this circle's diameter by 1 Planck length. Would the radius increase?

Are these true paradoxes, something that just happens at this level or do they not hold any water?

You seem to be mixing mathematics and physics. Planck length is a physics concept and the question you are raising is mathematical. In mathematics there is no smallest unit of distance.