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Circular map (Posted on 2006-11-15) Difficulty: 5 of 5
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    
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re(7): Full Proof | Comment 26 of 29 |
(In reply to re(6): Full Proof by Joel)

Thanks Joel. I was able to follow the proof easily.

Question: Is "If f maps circles to circles, then the inverse of f maps circles to circles" equivalent to "If f maps circles to circles, then it maps straight lines to straight lines"?

If it is, then would it have been easier or harder to prove?

 

Edited on December 19, 2006, 3:44 am

Edited on December 19, 2006, 3:11 pm
  Posted by Bractals on 2006-12-19 00:49:38

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