Talk:Parallel (geometry): Difference between revisions
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imported>Paul Wormer (→flat plane: new section) |
imported>Boris Tsirelson (→Two remarks: new section) |
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A plane is by definition a flat (zero curvature) surface in Euclidean space.--[[User:Paul Wormer|Paul Wormer]] 17:04, 25 March 2010 (UTC) | A plane is by definition a flat (zero curvature) surface in Euclidean space.--[[User:Paul Wormer|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. | |||
[[User:Boris Tsirelson|Boris Tsirelson]] 19:20, 27 March 2010 (UTC) | |||
Revision as of 13:21, 27 March 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)