Talk:Parallel (geometry): Difference between revisions
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imported>Paul Wormer |
imported>Peter Schmitt (→Non-Euclidean parallels: new section) |
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:::Thanks--[[User:Paul Wormer|Paul Wormer]] 15:26, 28 March 2010 (UTC) | :::Thanks--[[User:Paul Wormer|Paul Wormer]] 15:26, 28 March 2010 (UTC) | ||
== Non-Euclidean parallels == | |||
Boris, the WP article is only partially right. It is quite common to call all non-intersecting lines parallel (e.g., Hilbert). --[[User:Peter Schmitt|Peter Schmitt]] 21:22, 15 April 2010 (UTC) | |||
Revision as of 15:22, 15 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 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)