Two rectangles, neither of which will fit inside the other, are said to be incomparable. This is equivalent to one rectangle being both longer and narrower. At least seven and at most eight mutually incomparable rectangles are needed to tile a given rectangle (Wells 1991).
Incomparable Rectangles
See also
RectangleExplore with Wolfram|Alpha
References
Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 116-117, 1991.Referenced on Wolfram|Alpha
Incomparable RectanglesCite this as:
Weisstein, Eric W. "Incomparable Rectangles." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IncomparableRectangles.html