# What is the minimum number of lines needed to divide space into m regions?

What is the minimum number of hyperplanes needed to divide the space of $$\mathbf{R}^n$$ into $$m$$ regions? I know that for $$\mathbf{R}^2$$, if we denote $$f(m)$$ to be the minimum number of lines needed to divide the regions, then we get $$f(m)=f(m-1)+1+m-1$$ by assuming that the new lines intersect with all previous lines. That line is cut into $$m$$ new segments and each segments generate a new region.