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What do you call a rectangle whose width/height ratio is between $r$ and $1/r$?

I use the terminology "$r$-balanced rectangle". So, a $1$-balanced rectangle is a square, a $2$-balanced rectangle is a rectangle whose width/height ratio is between $1/2$ and $2$, etc., and an $\infty$-balanced rectangle is just any general rectangle.

Is there a more standard terminology?

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Why is that useful? It only makes sense to introduce terminology if you use something frequently and better even, if it's a fundamental concept. If it turns out to be fundamental in your work, go ahead and give it a name. But I've never encountered this elsewhere and I can't fathom what purpose it could serve. –  Raskolnikov Jun 21 '13 at 7:43
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I think it would be naïve to close this question just because no-one who has read this question has ever come across such a thing before. That is to say, noone who has read it known the answer...which is a flawed reason for closing! For all we know, these things do have a name and we just do not know it - and so we have a valid question... –  user1729 Jun 21 '13 at 8:37
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@Raskolnikov: You could go through the list of questions the OP asked to see example applications, e.g. in rectangularizing the square. –  MvG Jun 21 '13 at 9:18
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@Raskolnikov: It is a terminology question - no effort is needed by an answerer, and no the OP should not be required to give motivation! –  user1729 Jun 21 '13 at 9:24
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@MvG thank you! Just to give some motivation: my research is related to division of land resources between people. One of the reasonable constraints in dividing land resources is that each land plot should be a balanced rectangle, because an un-balanced rectangle (i.e. a very skinny or a very flat one) is not useful. –  Erel Segal Halevi Jun 21 '13 at 13:19

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The closest term I could find so far is fat rectangles. This term has some applications in computer geometry. See, for example:

  • Agarwal et al, Binary Space Partitions for Fat Rectangles, 2000
  • Tóth, Binary Space Partitions for Axis-Aligned Fat Rectangles, 2008

Links: http://www.citeulike.org/user/erelsegal-halevi/tag/fat-rectangles

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The term "aspect ratio" is sometimes used. By convention it is always bigger than 1, i.e. one always divides the longer side by the shorter. Then your 2-balanced rectangles have aspect ratio at most 2.

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Yes, I was looking for a terminology for a rectangle whose aspect ratio is at most 2. The references I found call it "2-fat rectangle". –  Erel Segal Halevi Jul 31 '13 at 21:55

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