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(2): Sticking by my guns by henry)

In fact, if we allow lines to be considered circles of infinite radius then we can disprove using a circle inversion :

http://en.wikipedia.org/wiki/Circle_inversion

So, it is false if lines are infinite radius circle, and I'm guessing true if they are not (but can't prove it)

Posted by Joel on 2006-11-24 01:30:34