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: Not a proof, but ... by Tristan)

Tristan:  As you point out, we need a function that maps all circles to another circle.  Your function maps most circles into something that is not a circle.  Also, it is not yet defined for any points on the Y axis that are not (0,1) or (0,-1).

Posted by Steve Herman on 2006-11-23 09:02:55