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On Sep 11, 2017, at 7:46 PM, brian whatcott <betwys1@sbcglobal.net> wrote:
Perhaps it would be helpful to creep up on a structure of irrational lengths - say a square of area 2. It is easy to specify rectangles of rational length that enclose slightly different areas: 7/5 and 10/7; 141/100 and 200/141; 1414 /1000 and 2000/1414 ; 14142136 /10000000 and 2000000/14142136 and so on.
Which reminds me that mathematicians may insist that a recurring fraction of this form: 1.9999... is identical to 2 see https://arxiv.org/abs/0811.0164
Brian W