Line - Revision history

DavidB4: Undo revision 1291644 by ATexan (talk)

2016-11-29T04:26:48Z

Undo revision 1291644 by ATexan (talk)

ATexan at 04:22, November 29, 2016

2016-11-29T04:22:50Z

BRichtigen: adding two points form

2008-12-20T13:18:09Z

adding two points form

Foxtrot: restoring, reordering, and adding to intro.

2008-07-17T11:56:15Z

restoring, reordering, and adding to intro.

Ed Poor: remove blather - what we need is a basic, workable definition

2008-07-17T01:37:51Z

remove blather - what we need is a basic, workable definition

Foxtrot: fixed links

2008-05-28T04:13:36Z

fixed links

Foxtrot: much more info

2008-05-28T04:11:19Z

much more info

Dewey: Punctuation.

2007-11-09T01:17:19Z

Punctuation.

SSchultz: Remove vandalism - That's enough, troll. Stop causing trouble

2007-11-09T01:08:27Z

Remove vandalism - That's enough, troll. Stop causing trouble

PathologicalMonsters: again, not vandalism; legitimate corrections.

2007-11-09T01:07:04Z

again, not vandalism; legitimate corrections.

@@ Line 19: / Line 19: @@
 Attempts at providing a rigorous, abstract definition usually face philosophical [[paradox]]es, such as [[Euclid]]'s contention that lines are objects with "breadthless length."  In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite [[radius]] of [[curvature]], yet both these definitions have philosophical flaws as well.
-Airports
 [[Category:Geometry]]

@@ Line 19: / Line 19: @@
 Attempts at providing a rigorous, abstract definition usually face philosophical [[paradox]]es, such as [[Euclid]]'s contention that lines are objects with "breadthless length."  In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite [[radius]] of [[curvature]], yet both these definitions have philosophical flaws as well.
+Airports
 [[Category:Geometry]]

@@ Line 5: / Line 5: @@
 Common mathematical representations of a line include:
-In 2 dimensions in the [[Cartesian plane]]:
+In two dimensions in the [[Cartesian plane]]:
 *Standard Form: ax + by + c = 0
 *Slope-Intercept Form: y = mx + b (where m is the [[slope]] of the line, b is the [[y-intercept]])
 *Point-Slope Form: (y - y<sub>0</sub>) = m(x - x<sub>0</sub>) (where m is the slope and (x<sub>0</sub>, y<sub>0</sub>) is a point on the line)
 In n dimensions in [[Cartesian coordinates]]:

← Older revision		Revision as of 11:56, July 17, 2008
Line 1:		Line 1:
−	The '''line''' is a basic [[geometry\|geometric]] [[shape]].	+	The '''line''' is a basic [[geometry\|geometric]] [[shape]]. It is a straight, [[breadth]]less figure that extends to [[infinity]] in both directions and consists of infinitely many points strung all in a row with no spaces or breaks.
		+
		+	A line that can be drawn on paper is not actually a line, but a representation of a line since it does not extend infinitely in both directions. Two [[point]]s determine a (unique) line which goes through them. A line can be broken down into finite [[line segment]]s.
		+
		+	Common mathematical representations of a line include:
		+
		+	In 2 dimensions in the [[Cartesian plane]]:
		+	*Standard Form: ax + by + c = 0
		+	*Slope-Intercept Form: y = mx + b (where m is the [[slope]] of the line, b is the [[y-intercept]])
		+	*Point-Slope Form: (y - y<sub>0</sub>) = m(x - x<sub>0</sub>) (where m is the slope and (x<sub>0</sub>, y<sub>0</sub>) is a point on the line)
		+
		+	In n dimensions in [[Cartesian coordinates]]:
		+	*Parametrized Vector Form: r(t) = <x<sub>0</sub>, y<sub>0</sub>,...> + t<x, y,...>
		+
		+	==Philosophical nature of the line==
		+
		+	The line is such an intuitive concept that most mathematicians think it escapes a formal, rigorous, and general definition. The definition above is unsatisfactory because adjectives such as "straight" are usually defined in terms of resembling lines. Other such intuitive concepts without rigorous definitions are the [[point]], the [[plane]], the [[set]], [[symmetry]], and [[infinity]].
		+
		+	Attempts at providing a rigorous, abstract definition usually face philosophical [[paradox]]es, such as [[Euclid]]'s contention that lines are objects with "breadthless length." In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite [[radius]] of [[curvature]], yet both these definitions have philosophical flaws as well.

	[[Category:Geometry]]		[[Category:Geometry]]

← Older revision		Revision as of 01:37, July 17, 2008
Line 1:		Line 1:
−	The '''line''' is a basic [[geometry\|geometric]] [[shape]]. It is such an intuitive concept that most mathematicians think it escapes a formal, general definition. Other such intuitive concepts are the [[point]], the [[plane]], the [[set]], [[symmetry]], and [[infinity]].	+	The '''line''' is a basic [[geometry\|geometric]] [[shape]].
−
−	Attempts at providing a rigorous, abstract definition usually face philosophical [[paradox]]es, such as [[Euclid]]'s contention that lines are objects with "breadthless length." In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite [[radius]] of [[curvature]], yet both these definitions have philosophical flaws as well.
−
−	~~A line that can be drawn on paper is not actually a line, but a representation of a line. Two points determine a line. A line can be broken down into finite [[line segment]]s.~~
−
−	~~Common mathematical representations of a line include:~~
−
−	~~In 2 dimensions in the [[Cartesian plane]]:~~
−	*Standard Form: ax + by + c = 0
−	*Slope-Intercept Form: y = mx + b (where m is the [[slope]] of the line, b is the [[y-intercept]])
−	*Point-Slope Form: (y - y<sub>0</sub>) = m(x - x<sub>0</sub>) (where m is the slope and (x<sub>0</sub>, y<sub>0</sub>) is a point on the line)
−
−	~~In n dimensions in [[Cartesian coordinates]]:~~
−	*Parametrized Vector Form: r(t) = <x<sub>0</sub>, y<sub>0</sub>,...> + t<x, y,...>

	[[Category:Geometry]]		[[Category:Geometry]]

@@ Line 1: / Line 1: @@
 The '''line''' is a basic [[geometry|geometric]] [[shape]]. It is such an intuitive concept that most mathematicians think it escapes a formal, general definition. Other such intuitive concepts are the [[point]], the [[plane]], the [[set]], [[symmetry]], and [[infinity]].
-Attempts at providing a rigorous, abstract definition usually face philosophical [[paradox]]es, such as [[Euclid]]'s contention that lines are objects with "breadthless length."  In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite [[radius of curvature]], yet both these definitions have philosophical flaws as well.
+Attempts at providing a rigorous, abstract definition usually face philosophical [[paradox]]es, such as [[Euclid]]'s contention that lines are objects with "breadthless length."  In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite [[radius]] of [[curvature]], yet both these definitions have philosophical flaws as well.
 A line that can be drawn on paper is not actually a line, but a representation of a line.  Two points determine a line.  A line can be broken down into finite [[line segment]]s.

← Older revision		Revision as of 01:17, November 9, 2007
Line 1:		Line 1:
−	A line was described by [[Euclid]] as having "breadthless length. This means that a line in infinitely long, but has no width. Lines can be considered as curves with infinite radius of curvature. A line that can be drawn on paper is not actually a line, but a representation of a line. Two points determine a line. A line can be broken down into finite [[line segment]]s.	+	A line was described by [[Euclid]] as having "breadthless length." This means that a line in infinitely long, but has no width. Lines can be considered as curves with infinite radius of curvature. A line that can be drawn on paper is not actually a line, but a representation of a line. Two points determine a line. A line can be broken down into finite [[line segment]]s.

	Common mathematical representations of a line include:		Common mathematical representations of a line include:

← Older revision		Revision as of 01:08, November 9, 2007
Line 1:		Line 1:
−	A ~~'''~~line~~'''~~ was described by [[Euclid]] as having "breadthless length." This means that a line in infinitely long, but has no width. Lines can be considered as curves with infinite radius of curvature. A line that can be drawn on paper is not actually a line, but a representation of a line. Two points determine a line. A line can be broken down into finite [[line segment]]s.	+	A line was described by [[Euclid]] as having "breadthless length. This means that a line in infinitely long, but has no width. Lines can be considered as curves with infinite radius of curvature. A line that can be drawn on paper is not actually a line, but a representation of a line. Two points determine a line. A line can be broken down into finite [[line segment]]s.

	Common mathematical representations of a line include:		Common mathematical representations of a line include:

← Older revision		Revision as of 01:07, November 9, 2007
Line 1:		Line 1:
−	A line was described by [[Euclid]] as having "breadthless length. This means that a line in infinitely long, but has no width. Lines can be considered as curves with infinite radius of curvature. A line that can be drawn on paper is not actually a line, but a representation of a line. Two points determine a line. A line can be broken down into finite [[line segment]]s.	+	A '''line''' was described by [[Euclid]] as having "breadthless length." This means that a line in infinitely long, but has no width. Lines can be considered as curves with infinite radius of curvature. A line that can be drawn on paper is not actually a line, but a representation of a line. Two points determine a line. A line can be broken down into finite [[line segment]]s.

	Common mathematical representations of a line include:		Common mathematical representations of a line include: