# Planck Length Paradox?

1. Oct 10, 2012

### 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?

2. Oct 10, 2012

### 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.

3. Oct 11, 2012

### mathman

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.

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