Talk:Parallel (geometry)

From Citizendium
Revision as of 13:21, 27 March 2010 by imported>Boris Tsirelson (→‎Two remarks: new section)
Jump to navigation Jump to search
This article is developing and not approved.
 Main Article
 Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
To learn how to update the categories for this article, see here. To update categories, edit the metadata template.
 Definition:  (of lines or planes) In elementary geometry: having no point in common. [d] [e]
Checklist and Archives
 Workgroup category:  Mathematics [Categories OK]
 Talk Archive:  none  English language variant:  British English

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)

Retrieved from "https://citizendium.org/wiki/index.php?title=Talk:Parallel_(geometry)&oldid=575993"