Talk:Parallel (geometry)

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Revision as of 15:22, 15 April 2010 by imported>Peter Schmitt (→‎Non-Euclidean parallels: new section)
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 Definition:  (of lines or planes) In elementary geometry: having no point in common. [d] [e]
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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)

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