Date: Fri, 7 Feb 1997 17:25:50 -0500
From: Alex Bogomolny
Dear Lin-sen:
A non-square plane may take different shapes. If you are talking of whatever might be an image of a conformal mapping, then the answer is readily available - just consider images of approximating curves under this conformal mapping.
Actually, you may consider any homeomorphism (1-1, continuous both ways function) of plane regions.
Does this answer your question?
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