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I'd like to know if an absolute scale invariant shape can be drawn on paper. just like the case that a circle is rotation invariant.

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If you want it all to fit on a finite sheet of paper, it must be a single point.

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    can you please describe in a bit more detail that how is it scale invariant ( like there is white area around a black point which as drawn, and upon zooming by some scale factor with zoom center at that point, ultimately i will be seeing all black area which was different from initial representation of point). – 2017-02-05
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    I'm talking about a mathematical point, which will still look like a point no matter how much you zoom in. – 2017-02-05