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."

Let Family-of-circles(X,Y) denote the set
of all circles passing through the points
X and Y.

If A and B are distinct points, then clearly
f is an injection of Family-of-circles(A,B)
into Family-of-circles(f(A),f(B)).

Our problem: to show that it is a surjection.

Posted by Bractals on 2006-11-24 10:53:29