Main Question or Discussion Point
Consider any two rectangles in the x-y plane. I have a book that asserts that the union of any two such rectangles is the DISJOINT union of AT MOST SIX rectangles. I've been sketching rectangles and simply can't come up with an example that demands SIX rectangles in the disjoint union. The most I can find is FIVE. Can someone come up with an example of two rectangles whose union is a disjoint union of six rectangles? Thanks!