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."

(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