Talk:Non-Euclidean geometry
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consider two lines in a plane that are both perpendicular to a third line. In Euclidean and hyperbolic geometry, the two lines are then parallel.
I am not at all happy with the above. As far as I know, in hyperbolic geometry two lines in a plane are either intersecting, or parallel, or ultraparallel. Two lines which are both perpendicular to a third line are ultraparallel, not parallel.
See e.g. http://s13a.math.aca.mmu.ac.uk/Geometry/M23Geom/NonEuclideanGeometry/NonEuclidean.html
I am concerned about the matter, also because the statement has been used (in translation) in the corresponding Swedish article.
Sebastjan
- This is a well known inconsistency in terminology. When specifically working with hyperbolic geometry, one does use the words parallel, ultraparallel, etc. However, when talking in general about geometry, such as in the above excerpt, parallel is taken to mean two lines that do not intersect. This shouldn't be a problem as long as this inconsistency is noted in the article on hyperbolic geometry; I'll check. --Chan-Ho Suh 12:18, Dec 16, 2004 (UTC)
When did 'debate' on parallel postulate begin?
From the history section:
- The debate that eventually led to the discovery of non-Euclidean geometries began almost as soon as Euclid's work Elements was written.
This slipped by me a couple times, but now I realized that this seems very suspicious. I can't think of any ancient Greek works debating or casting doubt, or whatever, on the parallel postulate. It seems to me that the debate, so to speak, began when Greek works, such as Euclid, were discovered by the Europeans. --Chan-Ho Suh 08:49, Dec 19, 2004 (UTC)