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)
Our problem: to show that it is a surjection.
Posted by Bractals
on 2006-11-24 10:53:29