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Circular map (Posted on 2006-11-15) Difficulty: 5 of 5
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."

See The Solution Submitted by JLo    
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re: Full Proof | Comment 20 of 29 |
(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
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