I am writing a peper about dividing a shape into rectangles, where the main issue is to make sure that the rectangles have a limited aspect ratio. I am looking for a clear, unambiguous term for such rectangles.
Initially I used the term "r-balanced rectangle", for a rectangle whose width/height ratio is between $r$ and $1/r$. However, I noticed that this term is used with different meanings in different papers, so I look for another term.
Recently I found the term "fat rectangle" in two papers: Agarwal et al., "Binary space partitions for fat rectangles": "the aspect ratio of each rectangle in S is at most $\alpha$ , for some constant $\alpha \ge 1$", and similarly in Csaba D. Tóth, "Binary Space Partitions for Axis-Aligned Fat Rectangles". In my paper I study different bounds on the aspect ratio, so I must add the ratio bound (r) to the term, so I thought of using the term "r-fat rectangle", however, when r is larger, the rectangle is thinner, so maybe the term "r-thin rectangle" is better.
On the other hand, the term "fat rectangle" is used in other papers with a slightly different meaning, for example, Joseph O'Rourke and Geetika Tewari, "Partitioning Orthogonal Polygons into Fat Rectangles in Polynomial Time": "the shortest rectangle side is maximized over all rectangles", i.e., fatness relates to the absolute dimension of the shortest side, and not to the aspect ratio.
What, in your opinion, is the best term to use? "r-balanced rectangle"? "r-fat rectangle"? "r-thin rectangle"? Some other name?