# how can I describe this using math

• Jul 16th 2013, 05:45 AM
uperkurk
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?
• Jul 16th 2013, 06:14 AM
topsquark
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
• Jul 16th 2013, 06:33 AM
uperkurk
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?
• Jul 17th 2013, 03:00 AM
topsquark
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