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 Circular map (Posted on 2006-11-15)
Let f be a one-to-one correspondence of the points in a plane. Prove or disprove the following statement:

"If f maps circles to circles, then it maps straight lines to straight lines."

 See The Solution Submitted by JLo No Rating

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 re(3): Full Proof | Comment 22 of 29 |
(In reply to re(2): Full Proof by Tristan)

`We have a bijection f that maps the plane Ponto the plane P' that also maps circles intocircles. Per your proof (WLOG) we have f(a,b) = (c,d) with f(0,1) = (0,1) andf(0,-1) = (0,-1). You want to show that fmaps the y-axis to the y-axis. To do thisyou must show a=0 <==> c=0. You pick points(0,0) and (0,2) in the P' plane and derive acontradiction. I would have derived thecontradiction differently, but I agree thatc=0 ==> a=0. My problem is we still need toshow that a=0 ==> c=0.`
` `

 Posted by Bractals on 2006-12-17 15:35:08

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