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Where can i find a correct proof of the following theorem of H.Hopf:

For every continuous curve $L$ in the plane with endpoints $A$ and $B$ such that distance $\vert AB \vert = 1$, and for any natural number $n$, there exists a chord (meaning a straight segment with endpoints on $L$) that is parallel to $AB$ and whose length equals $1/n$.

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  • $\begingroup$ I can't find the proof, but it is in "H. Hopf, Uber die Sehen ebener Kontinuen und die Schleifen geschlossener Wege, Commentarii Mathematici Helvetici IX (1936-37), 303-319". If I remember correctly. $\endgroup$ – S.C.B. Feb 15 '17 at 17:18
  • $\begingroup$ Very similar to this question. $\endgroup$ – Arthur Feb 15 '17 at 17:22

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