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I am looking for a manuscript of Max Dehn entitled "Beweis des Satzes, dass jedes geradlinige geschlossene Polygon ohne Doppelpunkte 'die Ebene in zwei Teile teilt'".

According to Heinrich Guggenheimer [1] the manuscript contains the first complete and correct proof of the Jordan curve theorem. I was unable to find an online version. Apparently, the manuscript is in Box 4RM129 at Briscoe center for American history, somewhere in Texas [2]. But there may be some copy that has circulated in the seventies. Does anyone has such a copy?

[1] https://www.maths.ed.ac.uk/~v1ranick/jordan/guggenheim.pdf

[2] https://txarchives.org/utcah/finding_aids/00192.xml (Wayback Machine](https://web.archive.org/web/20180531051738/https://legacy.lib.utexas.edu/taro/utcah/00192/cah-00192.html))

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  • $\begingroup$ The Briscoe center is at UT Austin. Try contacting a mathematician who works there; eg Cameron Gordon? $\endgroup$
    – Sam Nead
    Oct 23, 2019 at 11:47
  • $\begingroup$ To clarify, Dehn's proof is for the polygonal Jordan curve theorem. He was interested in deriving it from a small subset of Hilbert's axioms for geometry. $\endgroup$
    – John Stillwell
    Oct 23, 2019 at 15:49
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    $\begingroup$ Not directly relevant, but Hales has championed the view that Jordan's original proof was correct. mizar.org/trybulec65/4.pdf $\endgroup$
    – Timothy Chow
    Oct 23, 2019 at 20:23
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    $\begingroup$ At the time Hales wrote his paper, he was unaware of Guggenheimer's paper. I asked Hales about this. He said Guggenheimer had two objections. The first was that Jordan didn't prove the theorem for polygons. Hales discusses this point in his paper. The second objection (p 194) was, "What is missing is a proof that for a Jordan curve $x(t)$, $0\le t \le 1$, and $\delta>0$ there is an $\epsilon_0$ such that the segments $x(t_i) x(t_{i+1}), x(t_j) x(t_{j+1})$ of a polygon of vertices $x(t_0),\ldots,x(t_N)$ cannot intersect if $t_{k+1}-t_k<\epsilon\le\epsilon_0$ and $|x(t_{j+1})-x(t_i)| <\delta$." $\endgroup$
    – Timothy Chow
    Aug 18, 2020 at 18:33
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    $\begingroup$ But Hales addresses this in Section 4.2. Jordan never claims that the segments of a polygon cannot intersect. He (initially) allows the segments of the polygon to intersect, and page 93 of his proof describes a finite process of removing small loops from the polygon to make it simple. $\endgroup$
    – Timothy Chow
    Aug 18, 2020 at 18:36

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