I know nothing about geometry, but I found a function which seems to have something to do with geometry.
This function is, $$f(x,y,z) = \dfrac{(x,y,z)}{\sqrt{1 + x^2 + y^2 + z^2}}$$
where $x,y,z$ is the coordinates of $R^3$ and $(x,y,z)$ is a vector of these variables.
I recall from a PDE class many years ago that this has something to do with surface area. But I cannot immediately see the connection. Also it looks like the normalization of a vector, but I have no idea what the $1$ is doing in there.
Does anyone who deal with geometry see the connection between this function with some concepts such as path length, minimal surface, etc.?
