
Region B is inside the curve. This can be said because of an interesting
theorem about simple closed curves. All "inside" regions of such a curve
are separated from each other by an even number of lines. The same is true
of all "outside" regions. And any inside region is separated from any
outside region by an odd number of lines. Zero is considered an even
number, so if there are no lines between two regions, then of course they
will be part of the same "side," and our theorem still holds.
When we pass from any part of region A to any part of region B, along any
path, we cross an even number of lines. In the illustration one such path
is shown by the dotted line. As it can be seen the line crosses four
lines, an even number. So we can say with certainty that no matter what
the rest of this curve looks like, region B is also inside. 
