By a half-square I mean a rectangle which has the dimensions $ a \times 2a $ (as opposed to a square which has the dimensions $ 2a \times 2a $)
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Half-square looks good to me ;p. – Jan 18 '17 at 14:37
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"Rectangle" :p ${}{}{}{}{}{}$ – MPW Jan 18 '17 at 14:39
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5Or double-square. – Arthur Jan 18 '17 at 14:39
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1@mathbeing - half-diagonal looked good to me too. – Gallifreyan Jan 18 '17 at 14:39
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I upvoted your answer because it is good to know the technical name, and I understand your point. However, what I was trying to say with my above comment is that even if you don't use the real name in whatever you need to write, it suffices to specify what you're meaning by half-square and then use it. If you write a good paper with it you might even spread the terminology, given that the current one is not so established. – Jan 18 '17 at 14:47
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1@mathbeing - sure, but since English is not my native language, and I never read a lot of technical literature, I wanted to play safe. – Gallifreyan Jan 18 '17 at 15:08
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@Gallifreian - Half-square is good as far as the area goes, but I'd avoid "half-diagonal", since the ratio of diagonals in your example is square root of 8 to square root of 5. – Edward Porcella Jan 18 '17 at 17:30
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@EdwardPorcella By half-diagonal he means the line segment from the center of a rectangle to its corner. – Akiva Weinberger Jan 18 '17 at 17:32