Let $ f: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} $ be a bijective function. If the image of any circle under $ f $ is a circle, prove that the image of any straight line under $ f $ is a straight line.
A bijection from the plane to itself that takes a circle to a circle must take a straight line to a straight line.
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$\begingroup$
geometry
functions
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0I'm not sure if this was obtained from a book. However, someone in my group mentioned that this was a folklore result and that he had seen a proof of it in some article. None of the rest of us could find a proof ourselves, and that fellow had trouble remembering the article where he had seen the proof. – 2012-10-14
1 Answers
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This has the result (second page). I hope it's thorough enough to placate your curiosity...
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0Tha$n$ks! You've provided a very nice pancake indeed. – 2012-10-14