- #1
Eidos
- 108
- 1
I was just thinking:
If is the surface area of a level surface, S, and is the volume of an enclosed solid, V, shouldn't be the arclength of a function f(x)?
Lets say that our surface is given implicitly by
For the surface area we get:
=
where is the Jacobian determinant.
Now if we define function f implicitly by
=
Arclength is usually given by .
This works out the same;
say our function is y=f(x) then ,
whose modulus is exactly
Is this correct?
If
Lets say that our surface is given implicitly by
For the surface area we get:
where
Now if we define function f implicitly by
Arclength is usually given by
This works out the same;
say our function is y=f(x) then
Is this correct?