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."

When this problem was in the queue, I suggested that if straight lines are considered as circles of infinite curvature, the problem is obvious.

Of course, JLo shot my idea down, but I still like it!

Posted by Federico Kereki on 2006-11-15 18:02:49