Let
f be a
onetoone 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 Familyofcircles(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 Familyofcircles(A,B)
into Familyofcircles(f(A),f(B)).
Our problem: to show that it is a surjection.

Posted by Bractals
on 20061124 10:53:29 