Talk:Parallel (geometry): Difference between revisions
imported>Boris Tsirelson (→Non-Euclidean parallels: I did not know) |
imported>Howard C. Berkowitz (→Axiom or postulate?: new section) |
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:Really? I did not know. Well, if so, change it accordingly. [[User:Boris Tsirelson|Boris Tsirelson]] 05:20, 16 April 2010 (UTC) | :Really? I did not know. Well, if so, change it accordingly. [[User:Boris Tsirelson|Boris Tsirelson]] 05:20, 16 April 2010 (UTC) | ||
== Axiom or postulate? == | |||
Is the proper Euclidean term the "Parallel Axiom" or "Parallel Postulate"? I learned it as the latter, which I think is traditional although axiom would be more correct modern mathematical terminology. [[User:Howard C. Berkowitz|Howard C. Berkowitz]] 01:00, 17 April 2010 (UTC) | |||
Revision as of 19:00, 16 April 2010
flat plane
A plane is by definition a flat (zero curvature) surface in Euclidean space.--Paul Wormer 17:04, 25 March 2010 (UTC)
Two remarks
"do not cross at any point, not even at infinity" — in elementary texts there is no such notion as intersection at infinity; in non-elementary texts (say, projective geometry) such notion exists, and it appears that parallel lines do intersect at infinity.
"parallel lines satisfy a transitivity relation" — no, it is not, unless we agree that each line is parallel to itself.
Boris Tsirelson 19:20, 27 March 2010 (UTC)
- Please go ahead, fix it. --Paul Wormer 09:53, 28 March 2010 (UTC)
- I did. Boris Tsirelson 12:14, 28 March 2010 (UTC)
- Thanks--Paul Wormer 15:26, 28 March 2010 (UTC)
Non-Euclidean parallels
Boris, the WP article you cited is only partially right. It is quite common to call all non-intersecting lines parallel (e.g., Hilbert). --Peter Schmitt 21:22, 15 April 2010 (UTC)
- Really? I did not know. Well, if so, change it accordingly. Boris Tsirelson 05:20, 16 April 2010 (UTC)
Axiom or postulate?
Is the proper Euclidean term the "Parallel Axiom" or "Parallel Postulate"? I learned it as the latter, which I think is traditional although axiom would be more correct modern mathematical terminology. Howard C. Berkowitz 01:00, 17 April 2010 (UTC)