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 Sticking by my guns by Federico Kereki)

When you initially suggested that lines could be considered as a special type of circle, my first reaction was also that this would make the solution rather obvious. But now that I am reading it again, I am not so sure anymore. How exactly would this notion of straight lines allow for an obvious solution?

Of course, for this problem I am still insisting that straight lines are NOT circles, not even really large ones ;-)

Posted by JLo on 2006-11-16 12:35:32