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."

If a point can be considered a circle of zero radius, then the statement is disproven by the following.

Let f map everything in the plane to point P. f maps all circles and lines to P, which is a circle but not a line.

Posted by Bernie Hunt on 2006-11-16 10:13:08