Bisection method - Revision history

en>Wcherowi: Reverted to revision 623684243 by Jitse Niesen (talk): Intervening edits removed essential content. (TW)

2014-12-03T04:51:36Z

Reverted to revision 623684243 by Jitse Niesen (talk): Intervening edits removed essential content. (TW)

← Older revision		Revision as of 06:51, 3 December 2014
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	~~The author is known as Wilber Pegues. Since~~ I was ~~eighteen I've been operating as a bookkeeper but quickly my spouse and I will start our personal company~~. ~~The preferred hobby for him and his kids is to perform lacross~~ and ~~he would never give it up. For many years he's been residing in Alaska and he doesn't plan on altering it~~.<br><br>~~My homepage ... free psychic readings,~~ [http://~~Vjchary~~.com/~~success/?author=17500 http://Vjchary~~.~~com/success/?author=17500~~],		I am Angeline and was born on 21 October 1989. My hobbies are People watching and Fantasy Football.<br><br>Here is my weblog [http://www.daytradeforex.com/products.htm super easy forex trade]

en>Glrx: Undid revision 596360405 by 106.79.188.220 (talk) Chatty; imbedded link

2014-02-21T19:40:49Z

Undid revision 596360405 by 106.79.188.220 (talk) Chatty; imbedded link

← Older revision		Revision as of 21:40, 21 February 2014
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	~~In [[geometry]], a '''half-space'''~~ is ~~either of the two parts into which a [[plane (geometry)\|plane]] divides the three-dimensional [[Euclidean space]]~~. ~~More generally, a~~ '~~''half-space''' is either of the two parts into which~~ a ~~[[hyperplane]] divides an [[affine space]]~~. ~~That~~ is~~, the points that are not incident~~ to the hyperplane are [[partition (set theory)\|partitioned]] into two [[convex set]]s (i.e., half-spaces), such that any subspace connecting a point in one set to a point in the other must intersect the hyperplane.		The author is known as Wilber Pegues. Since I was eighteen I've been operating as a bookkeeper but quickly my spouse and I will start our personal company. The preferred hobby for him and his kids is to perform lacross and he would never give it up. For many years he's been residing in Alaska and he doesn't plan on altering it.<br><br>My homepage ... free psychic readings, [http://Vjchary.com/success/?author=17500 http://Vjchary.com/success/?author=17500],

	A half-space can be either ''open'' or ''closed''. An '''open half-space''' is either of the two [[open set]]s produced by the subtraction of a hyperplane from the affine space. A '''closed half-space''' is the union of an open half-space and ~~the hyperplane that defines~~ it.

	~~If the space is [[two-dimensional]], then a half-space is called a~~ '~~''half-plane''' (open or closed). A half-space~~ in ~~a [[one-dimensional]] space is called a '''[[Line_(mathematics)#Ray\|ray]]''~~'.

	~~A half-space may be specified by a linear inequality, derived from the [[linear equation]] that specifies the defining hyperplane.~~

	~~A strict linear [[inequality (mathematics)\|inequality]] specifies an open half-space:~~

	~~:<math>a_1x_1+a_2x_2+\cdots+a_nx_n>b</math>~~

	~~A non-strict one specifies a closed half-space:~~

	~~:<math>a_1x_1+a_2x_2+\cdots+a_nx_n\geq b</math>~~

	~~Here, one assumes that not all of the real numbers ''a''<sub>1</sub>, ''a''~~<~~sub~~>2<~~/sub~~>, ..., ~~''a''<sub>''n''<~~/~~sub> are zero~~.

	=~~=Properties==~~

	* A half-space is a [[convex set]].
	* Any [[convex set]] can be described as the (possibly infinite) intersection of half-spaces.

	~~==Upper and lower half-spaces==~~

	~~The open (closed) '''upper half-space''' is the half-space of all (''x''<sub>1<~~/~~sub>, ''x''<sub>2<~~/~~sub>,~~ .~~.., ''x''<sub>''n''<~~/~~sub>) such that ''x''<sub>''n''</sub> > 0 (≥ 0). The open (closed) '''lower half-space''' is defined similarly, by requiring that ''x''<sub>''n''<~~/~~sub> be negative (non-positive).~~

	~~==See also~~==
	* [[Half-line]]
	* [[Upper half-plane]]
	* [[Poincaré half-plane model]]
	* [[Siegel upper half-space]]
	* [[Nef polygon]] , ~~construction of [[polyhedra]] using half-spaces.~~

	~~==External links==~~
	* {{Mathworld \| urlname=Half-Space \| title=Half-Space }}

	~~{{DEFAULTSORT:Half-Space}}~~
	~~[[Category:Euclidean geometry]]~~

en>Glenn L: Reverted 2 edits by 180.233.122.180 (talk) to last revision by Jitse Niesen. (TW)

2014-01-31T10:21:39Z

Reverted 2 edits by 180.233.122.180 (talk) to last revision by Jitse Niesen. (TW)

← Older revision		Revision as of 12:21, 31 January 2014
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	~~Gabrielle~~ is ~~what her spouse loves~~ to ~~call your wife~~'s ~~though she [https://www~~.~~gov~~.~~uk/search?q=doesn%27t+undoubtedly doesn't undoubtedly~~] ~~like being~~ called ~~like this~~. As a ~~woman what your girl really likes~~ is ~~mah jongg but she hasn~~'~~t made~~ a ~~dime with it~~. ~~Software acquiring is where her first income comes from remember~~, ~~though~~ , ~~soon her husband but also her will start your own business~~. ~~For~~ a ~~while she~~'~~s happened to~~ be ~~in Massachusetts~~. ~~Go to her website to come out more: http:~~//~~circuspartypanama~~.~~com~~<br><br>~~Feel free to visit my blog; [http:~~//~~circuspartypanama~~.~~com clash~~ of ~~clans hack~~]		In [[geometry]], a '''half-space''' is either of the two parts into which a [[plane (geometry)\|plane]] divides the three-dimensional [[Euclidean space]]. More generally, a '''half-space''' is either of the two parts into which a [[hyperplane]] divides an [[affine space]]. That is, the points that are not incident to the hyperplane are [[partition (set theory)\|partitioned]] into two [[convex set]]s (i.e., half-spaces), such that any subspace connecting a point in one set to a point in the other must intersect the hyperplane.

			A half-space can be either ''open'' or ''closed''. An '''open half-space''' is either of the two [[open set]]s produced by the subtraction of a hyperplane from the affine space. A '''closed half-space''' is the union of an open half-space and the hyperplane that defines it.

			If the space is [[two-dimensional]], then a half-space is called a '''half-plane''' (open or closed). A half-space in a [[one-dimensional]] space is called a '''[[Line_(mathematics)#Ray\|ray]]'''.

			A half-space may be specified by a linear inequality, derived from the [[linear equation]] that specifies the defining hyperplane.

			A strict linear [[inequality (mathematics)\|inequality]] specifies an open half-space:

			:<math>a_1x_1+a_2x_2+\cdots+a_nx_n>b</math>

			A non-strict one specifies a closed half-space:

			:<math>a_1x_1+a_2x_2+\cdots+a_nx_n\geq b</math>

			Here, one assumes that not all of the real numbers ''a''<sub>1</sub>, ''a''<sub>2</sub>, ..., ''a''<sub>''n''</sub> are zero.

			==Properties==

			* A half-space is a [[convex set]].
			* Any [[convex set]] can be described as the (possibly infinite) intersection of half-spaces.

			==Upper and lower half-spaces==

			The open (closed) '''upper half-space''' is the half-space of all (''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''n''</sub>) such that ''x''<sub>''n''</sub> > 0 (≥ 0). The open (closed) '''lower half-space''' is defined similarly, by requiring that ''x''<sub>''n''</sub> be negative (non-positive).

			==See also==
			* [[Half-line]]
			* [[Upper half-plane]]
			* [[Poincaré half-plane model]]
			* [[Siegel upper half-space]]
			* [[Nef polygon]] , construction of [[polyhedra]] using half-spaces.

			==External links==
			* {{Mathworld \| urlname=Half-Space \| title=Half-Space }}

			{{DEFAULTSORT:Half-Space}}
			[[Category:Euclidean geometry]]

en>Glrx: /* External links */ article already has psuedo code

2012-07-24T17:21:31Z

External links: article already has psuedo code

New page

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