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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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Some Thoughts Family of Circles | Comment 18 of 29 |

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
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