Quantum concentration - Revision history

en>Yobot: Tagging using AWB (10703)

2015-01-07T13:37:55Z

Tagging using AWB (10703)

← Older revision		Revision as of 15:37, 7 January 2015
Line 1:		Line 1:
	~~[[File:Helixtgtdev.png\|thumb\|right\|300px\|The tangent developable of a helix]]~~		Claude is her name and she totally digs that name. The thing I adore most bottle tops gathering and now I have time to consider on new things. Her family lives in Idaho. His day occupation is a monetary officer but he ideas on changing it.<br><br>my page [http://Letuschaton.com/blogs/post/27011 extended car warranty]
	~~The '''tangent developable''' of a [[space curve]] <math>\gamma(t)</math>~~ is ~~a [[developable surface]] formed by the union of the [[tangent line]]s to the curve.~~

	~~==Parameterization==~~
	~~Let <math>\gamma(t)</math> be a parameterization of a smooth space curve. That is, <math>\gamma</math> is a [[differentiable function\|twice-differentiable function]] with nowhere-vanishing derivative~~ that maps its argument <math>t</math> (a [[real number]]) to a point in space; the curve is the image of <math>\gamma</math>. Then a two-dimensional surface, the tangent developable of <math>\gamma</math>, may be parameterized by the map
	~~:<math>(s,t)\mapsto \gamma(t) + s\gamma'(t)~~.~~</math><ref>{{citation~~
	~~\| last = Pressley \| first = Andrew~~
	~~\| isbn = 1-84882-890-X~~
	~~\| page = 129~~
	~~\| publisher = Springer~~
	~~\| title = Elementary Differential Geometry~~
	~~\| year = 2010}}.</ref>~~
	The ~~original curve forms a boundary of the tangent developable,~~ and ~~is called its directrix~~.

	~~==Properties==~~
	The tangent developable is a [[developable surface]]; that is, it is a surface with zero [[Gaussian curvature]]. It is one of three fundamental types of developable surface; the other two are the generalized cones (the surface traced out by a one-dimensional family ~~of lines through a fixed point), and the cylinders (surfaces traced out by a one-dimensional family of [[parallel lines]])~~. ~~(The [[plane (geometry)\|plane]]~~ is ~~sometimes given as a fourth type, or may be seen as~~ a ~~special case of either of these two types.) Every developable surface in three-dimensional space may be formed by gluing together pieces of these three types;~~ it ~~follows from this that every developable surface is a [[ruled surface]], a union of a one-dimensional family of lines~~.<~~ref name="lawrence"/~~> ~~However, not every ruled surface is developable; the [[helicoid]] provides a counterexample.~~

	~~==History==~~
	~~Tangent developables were first studied by [[Leonhard Euler]] in 1772.~~<~~ref~~>~~{{citation~~
	~~\| last = Euler \| first = L. \| author-link = Leonhard Euler~~
	~~\| journal = Novi Commentarii academiae scientiarum Petropolitanae~~
	~~\| language = Latin~~
	~~\| pages = 3–34~~
	~~\| title = De solidis quorum superficiem in planum explicare licet~~
	~~\| url =~~ http://~~www~~.~~math.dartmouth.edu~~/~~~euler/pages/E419.html~~
	~~\| volume = 16~~
	\| year = 1772}}.</ref> Until that time, the only known developable surfaces were the generalized cones and the cylinders. Euler showed that tangent developables are developable and that every developable surface is of one of these types.<ref name="lawrence">{{citation
	~~\| last = Lawrence \| first = Snežana~~
	~~\| doi = 10.1007~~/~~s00004-011-0087-z~~
	~~\| issue = 3~~
	~~\| journal = Nexus Network Journal~~
	~~\| pages = 701–714~~
	~~\| title = Developable surfaces: their history and application~~
	~~\| volume = 13~~
	~~\| year = 2011}}.<~~/~~ref>~~

	~~==References==~~
	~~{{reflist}}~~

	~~==External links==~~
	*{{MathWorld\|title=Tangent Developable\|urlname=TangentDevelopable}}

	~~{{DEFAULTSORT:Tangent Developable}}~~
	~~[[Category:Differential geometry of surfaces]]~~
	~~[[Category:Surfaces]~~]

en>Jason from nyc: wikilink author names

2013-12-10T15:22:37Z

wikilink author names

← Older revision		Revision as of 17:22, 10 December 2013
Line 1:		Line 1:
	~~Greetings. Allow me start over the counter std test by at~~ [~~http~~:~~//www~~.~~buzzbit.net~~/~~blog/288042 home std test~~] ~~std testing telling you~~ the ~~author'~~s ~~title - Phebe. Years ago we moved~~ to ~~Puerto Rico and my family members loves it~~. ~~Hiring has been my occupation for some over the [http:~~/~~/www~~.~~Feminist.com~~/~~resources~~/~~ourbodies~~/~~std~~.~~html counter std] test time but I~~'~~ve currently [http://www~~.~~care2.com~~/~~greenliving/5~~-~~myths~~-~~about~~-~~herpes~~.~~html utilized~~] ~~for an additional 1~~. ~~One~~ of the ~~very best issues in~~ the ~~world for me~~ is ~~to do aerobics and I've been performing~~ it ~~for fairly~~ a ~~whilst~~.<br><br>~~Here is my page: at [~~http://www.~~innovec~~.~~com~~/~~node~~/~~3171 home std test kit] std testing ([http:~~//~~i4p~~.~~info~~/~~article~~.~~php?id~~=~~114136 investigate this site~~])		[[File:Helixtgtdev.png\|thumb\|right\|300px\|The tangent developable of a helix]]
			The '''tangent developable''' of a [[space curve]] <math>\gamma(t)</math> is a [[developable surface]] formed by the union of the [[tangent line]]s to the curve.

			==Parameterization==
			Let <math>\gamma(t)</math> be a parameterization of a smooth space curve. That is, <math>\gamma</math> is a [[differentiable function\|twice-differentiable function]] with nowhere-vanishing derivative that maps its argument <math>t</math> (a [[real number]]) to a point in space; the curve is the image of <math>\gamma</math>. Then a two-dimensional surface, the tangent developable of <math>\gamma</math>, may be parameterized by the map
			:<math>(s,t)\mapsto \gamma(t) + s\gamma'(t).</math><ref>{{citation
			\| last = Pressley \| first = Andrew
			\| isbn = 1-84882-890-X
			\| page = 129
			\| publisher = Springer
			\| title = Elementary Differential Geometry
			\| year = 2010}}.</ref>
			The original curve forms a boundary of the tangent developable, and is called its directrix.

			==Properties==
			The tangent developable is a [[developable surface]]; that is, it is a surface with zero [[Gaussian curvature]]. It is one of three fundamental types of developable surface; the other two are the generalized cones (the surface traced out by a one-dimensional family of lines through a fixed point), and the cylinders (surfaces traced out by a one-dimensional family of [[parallel lines]]). (The [[plane (geometry)\|plane]] is sometimes given as a fourth type, or may be seen as a special case of either of these two types.) Every developable surface in three-dimensional space may be formed by gluing together pieces of these three types; it follows from this that every developable surface is a [[ruled surface]], a union of a one-dimensional family of lines.<ref name="lawrence"/> However, not every ruled surface is developable; the [[helicoid]] provides a counterexample.

			==History==
			Tangent developables were first studied by [[Leonhard Euler]] in 1772.<ref>{{citation
			\| last = Euler \| first = L. \| author-link = Leonhard Euler
			\| journal = Novi Commentarii academiae scientiarum Petropolitanae
			\| language = Latin
			\| pages = 3–34
			\| title = De solidis quorum superficiem in planum explicare licet
			\| url = http://www.math.dartmouth.edu/~euler/pages/E419.html
			\| volume = 16
			\| year = 1772}}.</ref> Until that time, the only known developable surfaces were the generalized cones and the cylinders. Euler showed that tangent developables are developable and that every developable surface is of one of these types.<ref name="lawrence">{{citation
			\| last = Lawrence \| first = Snežana
			\| doi = 10.1007/s00004-011-0087-z
			\| issue = 3
			\| journal = Nexus Network Journal
			\| pages = 701–714
			\| title = Developable surfaces: their history and application
			\| volume = 13
			\| year = 2011}}.</ref>

			==References==
			{{reflist}}

			==External links==
			*{{MathWorld\|title=Tangent Developable\|urlname=TangentDevelopable}}

			{{DEFAULTSORT:Tangent Developable}}
			[[Category:Differential geometry of surfaces]]
			[[Category:Surfaces]]

208.81.184.4: better wikilink

2012-03-19T16:00:51Z

better wikilink

New page

Greetings. Allow me start over the counter std test by at [http://www.buzzbit.net/blog/288042 home std test] std testing telling you the author's title - Phebe. Years ago we moved to Puerto Rico and my family members loves it. Hiring has been my occupation for some over the [http://www.Feminist.com/resources/ourbodies/std.html counter std] test time but I've currently [http://www.care2.com/greenliving/5-myths-about-herpes.html utilized] for an additional 1. One of the very best issues in the world for me is to do aerobics and I've been performing it for fairly a whilst.<br><br>Here is my page: at [http://www.innovec.com/node/3171 home std test kit] std testing ([http://i4p.info/article.php?id=114136 investigate this site])

← Older revision		Revision as of 15:37, 7 January 2015
Line 1:		Line 1:
	~~[[File:Helixtgtdev.png\|thumb\|right\|300px\|The tangent developable of a helix]]~~		Claude is her name and she totally digs that name. The thing I adore most bottle tops gathering and now I have time to consider on new things. Her family lives in Idaho. His day occupation is a monetary officer but he ideas on changing it.<br><br>my page [http://Letuschaton.com/blogs/post/27011 extended car warranty]
	~~The '''tangent developable''' of a [[space curve]] <math>\gamma(t)</math>~~ is ~~a [[developable surface]] formed by the union of the [[tangent line]]s to the curve.~~

	~~==Parameterization==~~
	~~Let <math>\gamma(t)</math> be a parameterization of a smooth space curve. That is, <math>\gamma</math> is a [[differentiable function\|twice-differentiable function]] with nowhere-vanishing derivative~~ that maps its argument <math>t</math> (a [[real number]]) to a point in space; the curve is the image of <math>\gamma</math>. Then a two-dimensional surface, the tangent developable of <math>\gamma</math>, may be parameterized by the map
	~~:<math>(s,t)\mapsto \gamma(t) + s\gamma'(t)~~.~~</math><ref>{{citation~~
	~~\| last = Pressley \| first = Andrew~~
	~~\| isbn = 1-84882-890-X~~
	~~\| page = 129~~
	~~\| publisher = Springer~~
	~~\| title = Elementary Differential Geometry~~
	~~\| year = 2010}}.</ref>~~
	The ~~original curve forms a boundary of the tangent developable,~~ and ~~is called its directrix~~.

	~~==Properties==~~
	The tangent developable is a [[developable surface]]; that is, it is a surface with zero [[Gaussian curvature]]. It is one of three fundamental types of developable surface; the other two are the generalized cones (the surface traced out by a one-dimensional family ~~of lines through a fixed point), and the cylinders (surfaces traced out by a one-dimensional family of [[parallel lines]])~~. ~~(The [[plane (geometry)\|plane]]~~ is ~~sometimes given as a fourth type, or may be seen as~~ a ~~special case of either of these two types.) Every developable surface in three-dimensional space may be formed by gluing together pieces of these three types;~~ it ~~follows from this that every developable surface is a [[ruled surface]], a union of a one-dimensional family of lines~~.<~~ref name="lawrence"/~~> ~~However, not every ruled surface is developable; the [[helicoid]] provides a counterexample.~~

	~~==History==~~
	~~Tangent developables were first studied by [[Leonhard Euler]] in 1772.~~<~~ref~~>~~{{citation~~
	~~\| last = Euler \| first = L. \| author-link = Leonhard Euler~~
	~~\| journal = Novi Commentarii academiae scientiarum Petropolitanae~~
	~~\| language = Latin~~
	~~\| pages = 3–34~~
	~~\| title = De solidis quorum superficiem in planum explicare licet~~
	~~\| url =~~ http://~~www~~.~~math.dartmouth.edu~~/~~~euler/pages/E419.html~~
	~~\| volume = 16~~
	\| year = 1772}}.</ref> Until that time, the only known developable surfaces were the generalized cones and the cylinders. Euler showed that tangent developables are developable and that every developable surface is of one of these types.<ref name="lawrence">{{citation
	~~\| last = Lawrence \| first = Snežana~~
	~~\| doi = 10.1007~~/~~s00004-011-0087-z~~
	~~\| issue = 3~~
	~~\| journal = Nexus Network Journal~~
	~~\| pages = 701–714~~
	~~\| title = Developable surfaces: their history and application~~
	~~\| volume = 13~~
	~~\| year = 2011}}.<~~/~~ref>~~

	~~==References==~~
	~~{{reflist}}~~

	~~==External links==~~
	*{{MathWorld\|title=Tangent Developable\|urlname=TangentDevelopable}}

	~~{{DEFAULTSORT:Tangent Developable}}~~
	~~[[Category:Differential geometry of surfaces]]~~
	~~[[Category:Surfaces]~~]