Talk:Plane (geometry)/Draft

locus of points
In the last sentence of the lead, I would include that the locus is considered in a space whose properties are assumed to be known (from elementary geometry.) --Peter Schmitt 23:19, 12 May 2010 (UTC)
 * What do you prefer, "locus of points" or "set of points"? Boris Tsirelson 05:39, 13 May 2010 (UTC)
 * I did not think of it, but you are right: "locus" is a technical term, and "set" is easier to understand. --Peter Schmitt 10:56, 13 May 2010 (UTC)
 * Really, I am not completely understanding the logic of this lead. Why Hilbert's contribution (and even non-Euclidean geometry) are here? Why not in the section "Axiomatic approach"? And especially, the text "The first axiom regarding the plane is axiom I4: Three points A, B, C that are not on one and the same line determine always a plane &alpha;. He adds that this is expressed as "A, B, and C lie in &alpha;", or "A, B, and C are points of &alpha;". His axiom I5 is a subtle extension of I4: Any three points in plane &alpha; that are not on one line determine plane &alpha;", is it relevant enough? And, not completely unrelated question: what is your impression of my lead to "Line (geometry)"? Boris Tsirelson 11:55, 13 May 2010 (UTC)
 * By the way, all these "includeonly" inserted for the "Draft of the week", probably they should now be removed? Boris Tsirelson 11:58, 13 May 2010 (UTC)

Definition via lines
I have moved the figure to this place. It is not ideal (and could be replaced later: Tom has departed, so we cannot ask him to change it) but sufficient, if the description is adapted to use A,B,C accordingly. --Peter Schmitt 11:18, 13 May 2010 (UTC)
 * I'll better make another picture, wait about two days. Boris Tsirelson 12:01, 13 May 2010 (UTC)
 * I did. Boris Tsirelson 08:08, 14 May 2010 (UTC)

plane geometry
rectilinear or piecewise-linear or both? --Peter Schmitt 22:30, 13 May 2010 (UTC)
 * Surely not "rectilinear". Really, this text
 * "A plane figure is a combination of points and/or lines that fall on the same plane. In plane geometry every figure is plane, in contrast to solid geometry.


 * A rectilinear figure is a plane figure consisting of points, straight lines and straight line segments only. Rectilinear figures include triangles and polygons."
 * is not mine; I did not edit it at all, and in fact, I do not agree with it. Is it needed at all? Boris Tsirelson 10:30, 14 May 2010 (UTC)


 * Oops, sorry, I am cheating. I did edit it. Before me it was:
 * "A plane figure is a combination of points and/or lines that fall on the same plane.
 * A rectilinear figure is a plane figure consisting of straight lines only. Rectilinear figures include triangles and polygons. But anyway: Is it needed at all? Boris Tsirelson 10:44, 14 May 2010 (UTC)

modern approach
To exclude other uses of affine space, it should probably be real affine space. --Peter Schmitt 22:34, 13 May 2010 (UTC)
 * Fixed. Boris Tsirelson 10:34, 14 May 2010 (UTC)

beyond mathematics
"made close to ... a finite part/subset of a plane", only --Peter Schmitt 23:06, 13 May 2010 (UTC)


 * Fixed. Boris Tsirelson 10:36, 14 May 2010 (UTC)

Definition via right angles
What do you think of doing this as in "Line" (using triangles)? --Peter Schmitt 23:33, 5 June 2010 (UTC)


 * In "Line" I use "orthogonality in disguise" because I am afraid the usual orthogonality would raise objections: "you cannot introduce angles before lines". But in "Plane" there is no such problem: lines may be introduced before planes. Do you really want to see "orthogonality in disguise" in "Plane"? In addition to the orthogonality used now, or instead of it? Boris Tsirelson 09:00, 6 June 2010 (UTC)


 * Not necessarily. I just wondered why you avoided right angles in Line, but not here. I can see it now. I am not sure if some comment on this should be added (and what) --Peter Schmitt 10:40, 6 June 2010 (UTC)


 * By the way, a number of my questions (in sections above) are waiting for your answer... Boris Tsirelson 21:21, 8 June 2010 (UTC)