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Topic: easiest proof of Jordan Curve Theorem as a corollary of Moebius
theorem #1982 Correcting Math

Replies: 7   Last Post: Aug 11, 2014 3:19 PM

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Posts: 18,572
Registered: 3/31/08
I probably have the first NON flawed proof of the Jordan Curve
Theorem #1984 Correcting Math

Posted: Aug 10, 2014 4:49 PM
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Now unless I post this contentious issue of whether anyone proved the Jordan Curve theorem or that all of them were flawed, that future readers of AP will think I was making this up or exaggerating. But no, the JCT is questionable that anyone gave a sound proof. That is why my proof is all that more remarkable in that I take the Moebius Theorem proof and find the Jordan Curve proof as a minor corollary of Moebius.

--- quoting from Wikipedia on the contentious issue of whether anyone really had a proof of the Jordan Curve theorem or all of them were flawed ---

The Jordan curve theorem is named after the mathematician Camille Jordan, who found its first proof. For decades, mathematicians generally thought that this proof was flawed and that the first rigorous proof was carried out by Oswald Veblen. However, this notion has been challenged by Thomas C. Hales and others.
The first proof of this theorem was given by Camille Jordan in his lectures on real analysis, and was published in his book Cours d'analyse de l'École Polytechnique.[1] There is some controversy about whether Jordan's proof was complete: the majority of commenters on it have claimed that the first complete proof was given later by Oswald Veblen, who said the following about Jordan's proof:
His proof, however, is unsatisfactory to many mathematicians. It assumes the theorem without proof in the important special case of a simple polygon, and of the argument from that point on, one must admit at least that all details are not given.[2]

--- end quote ---


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