Suppose I have a closed connected bounded region $A$ in $R^2$ (I am not that familiar with definitions in topology, so I just use the word "region" to mean the obvious one). It's probably called a closed connected bounded set in $R^2$, is it not?
If I want to partition $A$ into $n+1$ subregions with equal area using $n$ vertical lines, where $n$ is even, how do I do that?
I mean, I am sure it can be done, but I'd like to find these exact lines. My first guess is I have to find the parametrization $(x(t),y(t))$ of the boundary, but I don't know where to go next, but my next guess is to use the concept of line integral.
I assume even $n$ since I guess it is a bit more complicated than the odd ones. Just maybe..
*feel free to change the tags