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 and B are distinct points, then they determine a line m. f(A) and f(B) are distinct points that determine a line n. When you say that f maps lines to lines do you mean

n = { f(P) | P in m }

        or

{ f(P) | P in m } is a subset of n ?

Edited on November 16, 2006, 5:41 pm

Posted by Bractals on 2006-11-16 17:37:48