Math Help - how can I describe this using math

1. how can I describe this using math

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

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 $5.077\times10^{-35}$ (planck length)
Circumference of $1.594986590227538\times10^{-34}$
Area of $2.0244367296463024\times10^{-69}$

Is this correct?

2. Re: how can I describe this using math

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

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 $5.077\times10^{-35}$ (planck length)
Circumference of $1.594986590227538\times10^{-34}$
Area of $2.0244367296463024\times10^{-69}$

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 $\lim_{r \to 0} \rho \to \infty$. It's the most valid expression I can come up with based on your description.

-Dan

3. Re: how can I describe this using math

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 $\lim_{r \to 0} \rho \to \infty$. 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?

4. Re: how can I describe this using math

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