how can I describe this using math

I want to describe using math notation. I have a sphere with circumference $\displaystyle c$ and density $\displaystyle d$ and as the circumference approaches $\displaystyle 0$, the density approaches $\displaystyle \infty$

Edit - I think I mean circumference.

On a little side note, assuming planck length is accurate would it mean that the smallest possible sphere that still obeys the laws of physics be:

Diameter of $\displaystyle 5.077\times10^{-35}$ (planck length)

Circumference of $\displaystyle 1.594986590227538\times10^{-34}$

Area of $\displaystyle 2.0244367296463024\times10^{-69}$

Is this correct?

Re: how can I describe this using math

Quote:

Originally Posted by

**uperkurk** I want to describe using math notation. I have a sphere with circumference $\displaystyle c$ and density $\displaystyle d$ and as the circumference approaches $\displaystyle 0$, the density approaches $\displaystyle \infty$

Edit - I think I mean circumference.

On a little side note, assuming planck length is accurate would it mean that the smallest possible sphere that still obeys the laws of physics be:

Diameter of $\displaystyle 5.077\times10^{-35}$ (planck length)

Circumference of $\displaystyle 1.594986590227538\times10^{-34}$

Area of $\displaystyle 2.0244367296463024\times10^{-69}$

Is this correct?

I would use radius or diameter instead of circumference, and the Plank scales (as I recall) define a black hole, but really there is no real physical significance to therm.

For your sphere I guess you could say $\displaystyle \lim_{r \to 0} \rho \to \infty$. It's the most valid expression I can come up with based on your description.

-Dan

Re: how can I describe this using math

Quote:

Originally Posted by

**topsquark** I would use radius or diameter instead of circumference, and the Plank scales (as I recall) define a black hole, but really there is no real physical significance to therm.

For your sphere I guess you could say $\displaystyle \lim_{r \to 0} \rho \to \infty$. It's the most valid expression I can come up with based on your description.

-Dan

Thanks, what is the lim thing? As the limit of r goes to 0, the limit of p goes to infinity?

Re: how can I describe this using math

Quote:

Originally Posted by

**uperkurk** Thanks, what is the lim thing? As the limit of r goes to 0, the limit of p goes to infinity?

Yup.

-Dan