@johncarlosbaez

it's a bit of a combinatorial exercise but i think if you start with all aspect ratios positive you end up with the rectangles all neatly adding up to the square/rectangle being dissected
(in some sense this feels like it has to be true "algebraically" if you express the area of each rectangle as (x_i-x_j)(y_k-y_l) and consider the sum of these as polynomials in the x_is, y_js)