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Jun 2, 2019 at 10:13 comment added Pietro Majer I have the impression that any definition of canonical should refer to a choice to be made in several analogous situations, following a rule. So I would agree with the definition of "canonical circle" in your example in that it refers to certain implicitly assumed principles of choices: "the canonical sphere of a normed space is the sphere centered at the origin with radius $1$"; "the canonical $n$-dimensional normed space is $\mathbb{R}^n$ with the Euclidean norm".
Jun 5, 2012 at 15:54 history edited Patrick I-Z CC BY-SA 3.0
added 385 characters in body; added 141 characters in body
Jun 4, 2012 at 21:40 history answered Patrick I-Z CC BY-SA 3.0