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 Full Proof by Tristan)

Given two distinct points A and B.
Your proof shows that if Y is a point
on Line(f(A),f(B)), then f^(-1)(Y) is
a point on Line(A,B). How do you show
that if X is a point on Line(A,B), then
f(X) is a point on Line(f(A),f(B))? 

Posted by Bractals on 2006-12-15 18:15:42