14
$\begingroup$

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.

  • 2
    Where is this problem from?2012-10-14
  • 0
    This problem was a question some of my classmates and I discussed over tea-time. We have regular discussions like this. Have you seen it somewhere before?2012-10-14
  • 0
    Mostly I'm wondering if you happen to know for a fact that this is true (e.g. because it was stated in a book of problems somewhere) or just believe it to be true.2012-10-14
  • 0
    I'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 1

6

This has the result (second page). I hope it's thorough enough to placate your curiosity...

  • 0
    Thanks! You've provided a very nice pancake indeed.2012-10-14