Talk:Line (Euclidean geometry)/Archive 1: Difference between revisions
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imported>Boris Tsirelson (→Lead: I shall try) |
imported>Boris Tsirelson (→Betweenness: which "at least") |
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The two conditions assume "three different points", thus the "at least" could be omitted. --[[User:Peter Schmitt|Peter Schmitt]] 23:18, 11 May 2010 (UTC) | The two conditions assume "three different points", thus the "at least" could be omitted. --[[User:Peter Schmitt|Peter Schmitt]] 23:18, 11 May 2010 (UTC) | ||
:Sorry, I do not understand which "at least" do you mean. | |||
:"If three different points belong to the given set then at least one of them lies between the others" — if you mean this, well, I can delete "at least"; it will be a bit less formal but still clear. | |||
:"If one of three different points lies between the others, and at least two of the three points belong to the given set, then the third point also belongs to the given set" — here "at least" is really essential, see Remark 3. | |||
[[User:Boris Tsirelson|Boris Tsirelson]] 06:00, 12 May 2010 (UTC) | |||
== Definition via right angles == | == Definition via right angles == | ||
A link to [[Pythagorean theorem]] seems to be appropriate. --[[User:Peter Schmitt|Peter Schmitt]] 23:41, 11 May 2010 (UTC) | A link to [[Pythagorean theorem]] seems to be appropriate. --[[User:Peter Schmitt|Peter Schmitt]] 23:41, 11 May 2010 (UTC) | ||
Revision as of 00:01, 12 May 2010
Rather cryptic
"The following demonstrates a line:
Given a line AC Point B is on AC ABC is the same line AC"
— rather cryptic; what could it mean? Boris Tsirelson 19:39, 27 March 2010 (UTC)
Lead
Boris, could you provide a short lead? If I do it then I will probably not be allowed to approve it. Somewhere the long form "straight line" should also be mentioned. --Peter Schmitt 23:07, 11 May 2010 (UTC)
- I shall try. Boris Tsirelson 05:53, 12 May 2010 (UTC)
Betweenness
The two conditions assume "three different points", thus the "at least" could be omitted. --Peter Schmitt 23:18, 11 May 2010 (UTC)
- Sorry, I do not understand which "at least" do you mean.
- "If three different points belong to the given set then at least one of them lies between the others" — if you mean this, well, I can delete "at least"; it will be a bit less formal but still clear.
- "If one of three different points lies between the others, and at least two of the three points belong to the given set, then the third point also belongs to the given set" — here "at least" is really essential, see Remark 3.
Boris Tsirelson 06:00, 12 May 2010 (UTC)
Definition via right angles
A link to Pythagorean theorem seems to be appropriate. --Peter Schmitt 23:41, 11 May 2010 (UTC)