Talk:Pasch's theorem

Cut and Paste
This stub is a cut and paste copy of the given reference. Worse, it tells nothing about the subject; it provides no context. I don't argue for deletion of this obvious copyvio; rather, an article must be written.

Why is this useful or important and in what way? &mdash; Xiong &#29066; talk * 23:38, 29 January 2008 (UTC)

This theorem by Pasch is used in Neutral Geometry ( Geometry without Euclid's Parallel Postulate ). It is a fundamental axiom for proving certain properties of line segments, and is also useful in other applications of Between-ness. There is more guidance in Greenberg's Geometry text. I will need to do a proper citation later. Kuttaka (talk) 17:49, 14 July 2009 (UTC)

I was searching for the proof, but i only found two articles: and. These things proove Hilbert's axioms II. 5 And not the one related to II. 4. Which one is the real Pasch theorem? This page [] is also affected. --Gabor8888 (talk) 22:08, 13 February 2010 (UTC)

Clarification needed
The lead currently begins


 * In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result of Euclidean geometry which cannot be derived from Euclid's postulates.

On the face of it this is self-contradictory. There needs to be a clarification of what is meant here by "Euclidean geometry", which to me means "geometry derivable from Euclid's postulates". Loraof (talk) 15:57, 7 December 2015 (UTC)


 * You are right, this needs fixing. We could add the clause, "thus showing that the original set of postulates needed to be expanded" or something like that. I had not fixed this myself because I got side-tracked into the issue of who actually calls this result Pasch's theorem. Since my comments above I have tracked down a fairly authoritative source who used this term in several papers. When I asked about the origins of the term he ultimately admitted that he could find no previous citations for it. In his work, Pasch's theorem is not the result given in this article. I am pretty sure that this is another example of something that sounded right but has no actual reliable source to back it up − but I haven't been able to prove that to my own satisfaction yet. Bill Cherowitzo (talk) 17:03, 7 December 2015 (UTC)


 * It seems to me that this is not a "result" at all, but rather a postulate. Loraof (talk) 20:15, 7 December 2015 (UTC)


 * Personally, all these betweeness results, out of context, look like postulates to me. What one calls a postulate versus a result depends on the author's development of the topic, so you can't really tell one from the other without a "scorecard". If we ever do track this down, the context will have to be part of the article. Bill Cherowitzo (talk) 20:07, 9 December 2015 (UTC)