Sieve analysis - Revision history

en>Monkbot: /* Types of sieves */Task 6k: add |script-title=; replace {{xx icon}} with |language= in CS1 citations; clean up language icons;

2015-01-05T17:04:49Z

Types of sieves: Task 6k: add |script-title=; replace {{xx icon}} with |language= in CS1 citations; clean up language icons;

← Older revision		Revision as of 19:04, 5 January 2015
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	Nice to meet you, my title is Ling and I totally dig that ~~name~~. Her ~~family members lives in Delaware~~ but she ~~needs to transfer simply because of her family. The thing I adore most bottle tops collecting~~ and ~~now I have time~~ to ~~consider on new things~~. ~~The occupation he~~'s been ~~occupying for years~~ is ~~a messenger~~.<br><br>Also visit my ~~page;~~ [http://~~Www~~.~~chillister~~.~~com~~/~~blogs~~/~~post~~/~~27388 extended car warranty~~]		Nice to meet you, my title is Ling and I totally dig that title. Her buddies say it's not great for her but what she enjoys performing is flower arranging and she is attempting to make it a profession. For many years she's been living in Kansas. Managing individuals is what I do in my working day job.<br><br>Also visit my blog: extended car warranty ([http://Holder11.dothome.co.kr/xe/center/733564 you can try this out])

en>Slazenger: Reverted 3 edits by 103.27.8.42 and 96.11.61.34 to last revision by ClueBot NG (HG)

2014-02-12T13:29:42Z

Reverted 3 edits by 103.27.8.42 and 96.11.61.34 to last revision by ClueBot NG (HG)

← Older revision		Revision as of 15:29, 12 February 2014
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	~~[[Image:Barrow inequality.svg\|thumb\|right\|300px]]~~		Nice to meet you, my title is Ling and I totally dig that name. Her family members lives in Delaware but she needs to transfer simply because of her family. The thing I adore most bottle tops collecting and now I have time to consider on new things. The occupation he's been occupying for years is a messenger.<br><br>Also visit my page; [http://Www.chillister.com/blogs/post/27388 extended car warranty]

	~~In [[geometry]]~~, ~~'''Barrow's inequality'''~~ is ~~an [[Inequality (mathematics)\|inequality]] relating the [[Euclidean distance\|distances]] between an arbitrary point within a [[triangle]], the vertices of the triangle,~~ and ~~certain points on the sides of the triangle~~.

	~~==Statement==~~
	Let ''P'' be an arbitrary point inside the [[triangle]] ''ABC''. From ''P'' and ''ABC'', define ''U'', ''V'', and ''W'' as the points where the [[angle bisector]]s of ''BPC'', ''CPA'', and ''APB'' intersect the sides ''BC'', ''CA'', ''AB'', respectively. Then Barrow's inequality states that

	~~: <math>PA+PB+PC\geq 2(PU+PV+PW),\,</math>~~

	~~with equality holding only~~ in ~~the case~~ of ~~an [[equilateral triangle]]~~.

	~~==History==~~
	~~Barrow's inequality strengthens the [[Erdős–Mordell inequality]], which has identical form except with ''PU'', ''PV'',~~ and ~~''PW'' replaced by the three distances of ''P'' from the triangle~~'s ~~sides. It~~ is ~~named after [[David Francis Barrow]]. Barrow's proof of this inequality was published in 1937, as his solution to~~ a ~~problem posed in the [[American Mathematical Monthly]] of proving the Erdős–Mordell inequality~~.<~~ref~~>~~{{citation~~
	~~\| last1 = Erdős \| first1 = Paul \| author1-link = Paul Erdős~~
	~~\| last2 = Mordell \| first2 = L. J. \| author2-link = Louis J. Mordell~~
	~~\| last3 = Barrow \| first3 = David F. \| author3-link = David Francis Barrow~~
	~~\| issue = 4~~
	~~\| journal = [[American Mathematical Monthly]]~~
	~~\| jstor = 2300713~~
	~~\| pages = 252–254~~
	~~\| title = Solution to problem 3740~~
	~~\| volume = 44~~
	~~\| year = 1937}}.</ref> A simpler proof was later given by Mordell.~~<~~ref~~>~~{{citation~~
	~~\| last = Mordell \| first = L. J. \| author-link = Louis J. Mordell~~
	~~\| issue = 357~~
	~~\| journal = Mathematical Gazette~~
	~~\| jstor = 3614019~~
	~~\| pages = 213–215~~
	~~\| title = On geometric problems of Erdös and Oppenheim~~
	~~\| volume = 46~~
	~~\| year = 1962}}.</ref>~~

	~~== See also ==~~
	* [[Euler's theorem in geometry]]

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

	~~==External links==~~
	*[http://~~www~~.~~eleves~~.~~ens.fr/home/kortchem~~/~~olympiades~~/~~Cours~~/~~Inegalites/tin2006.pdf Hojoo Lee: Topics in Inequalities - Theorems and Techniques]~~

	~~[[Category:Triangle geometry]]~~
	~~[[Category:Geometric inequalities]~~]

96.11.61.34: /* Air Jet Sieving */

2013-04-15T20:48:17Z

Air Jet Sieving

← Older revision		Revision as of 22:48, 15 April 2013
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	~~The writer~~ is ~~called Araceli Gulledge~~. ~~Delaware~~ is the ~~location I love most but I require~~ to ~~move for my family~~. ~~Playing croquet is something I will~~ by ~~no means give up. Interviewing is what she does~~.<br><br>~~Also visit my weblog :: auto warranty;~~ [http://~~Www~~.~~Newsfortrader~~.~~com~~/~~ActivityFeed~~/~~MyProfile~~/~~tabid~~/60/~~userId~~/~~29712/language/it~~-~~IT/Default.aspx mouse click the following web page~~],		[[Image:Barrow inequality.svg\|thumb\|right\|300px]]

			In [[geometry]], '''Barrow's inequality''' is an [[Inequality (mathematics)\|inequality]] relating the [[Euclidean distance\|distances]] between an arbitrary point within a [[triangle]], the vertices of the triangle, and certain points on the sides of the triangle.

			==Statement==
			Let ''P'' be an arbitrary point inside the [[triangle]] ''ABC''. From ''P'' and ''ABC'', define ''U'', ''V'', and ''W'' as the points where the [[angle bisector]]s of ''BPC'', ''CPA'', and ''APB'' intersect the sides ''BC'', ''CA'', ''AB'', respectively. Then Barrow's inequality states that

			: <math>PA+PB+PC\geq 2(PU+PV+PW),\,</math>

			with equality holding only in the case of an [[equilateral triangle]].

			==History==
			Barrow's inequality strengthens the [[Erdős–Mordell inequality]], which has identical form except with ''PU'', ''PV'', and ''PW'' replaced by the three distances of ''P'' from the triangle's sides. It is named after [[David Francis Barrow]]. Barrow's proof of this inequality was published in 1937, as his solution to a problem posed in the [[American Mathematical Monthly]] of proving the Erdős–Mordell inequality.<ref>{{citation
			\| last1 = Erdős \| first1 = Paul \| author1-link = Paul Erdős
			\| last2 = Mordell \| first2 = L. J. \| author2-link = Louis J. Mordell
			\| last3 = Barrow \| first3 = David F. \| author3-link = David Francis Barrow
			\| issue = 4
			\| journal = [[American Mathematical Monthly]]
			\| jstor = 2300713
			\| pages = 252–254
			\| title = Solution to problem 3740
			\| volume = 44
			\| year = 1937}}.</ref> A simpler proof was later given by Mordell.<ref>{{citation
			\| last = Mordell \| first = L. J. \| author-link = Louis J. Mordell
			\| issue = 357
			\| journal = Mathematical Gazette
			\| jstor = 3614019
			\| pages = 213–215
			\| title = On geometric problems of Erdös and Oppenheim
			\| volume = 46
			\| year = 1962}}.</ref>

			== See also ==
			* [[Euler's theorem in geometry]]

			==References==
			{{reflist}}

			==External links==
			*[http://www.eleves.ens.fr/home/kortchem/olympiades/Cours/Inegalites/tin2006.pdf Hojoo Lee: Topics in Inequalities - Theorems and Techniques]

			[[Category:Triangle geometry]]
			[[Category:Geometric inequalities]]

84.0.32.18: Deleted dead and spam external links

2012-08-11T15:48:45Z

Deleted dead and spam external links

New page

The writer is called Araceli Gulledge. Delaware is the location I love most but I require to move for my family. Playing croquet is something I will by no means give up. Interviewing is what she does.<br><br>Also visit my weblog :: auto warranty; [http://Www.Newsfortrader.com/ActivityFeed/MyProfile/tabid/60/userId/29712/language/it-IT/Default.aspx mouse click the following web page],

← Older revision		Revision as of 15:29, 12 February 2014
Line 1:		Line 1:
	~~[[Image:Barrow inequality.svg\|thumb\|right\|300px]]~~		Nice to meet you, my title is Ling and I totally dig that name. Her family members lives in Delaware but she needs to transfer simply because of her family. The thing I adore most bottle tops collecting and now I have time to consider on new things. The occupation he's been occupying for years is a messenger.<br><br>Also visit my page; [http://Www.chillister.com/blogs/post/27388 extended car warranty]

	~~In [[geometry]]~~, ~~'''Barrow's inequality'''~~ is ~~an [[Inequality (mathematics)\|inequality]] relating the [[Euclidean distance\|distances]] between an arbitrary point within a [[triangle]], the vertices of the triangle,~~ and ~~certain points on the sides of the triangle~~.

	~~==Statement==~~
	Let ''P'' be an arbitrary point inside the [[triangle]] ''ABC''. From ''P'' and ''ABC'', define ''U'', ''V'', and ''W'' as the points where the [[angle bisector]]s of ''BPC'', ''CPA'', and ''APB'' intersect the sides ''BC'', ''CA'', ''AB'', respectively. Then Barrow's inequality states that

	~~: <math>PA+PB+PC\geq 2(PU+PV+PW),\,</math>~~

	~~with equality holding only~~ in ~~the case~~ of ~~an [[equilateral triangle]]~~.

	~~==History==~~
	~~Barrow's inequality strengthens the [[Erdős–Mordell inequality]], which has identical form except with ''PU'', ''PV'',~~ and ~~''PW'' replaced by the three distances of ''P'' from the triangle~~'s ~~sides. It~~ is ~~named after [[David Francis Barrow]]. Barrow's proof of this inequality was published in 1937, as his solution to~~ a ~~problem posed in the [[American Mathematical Monthly]] of proving the Erdős–Mordell inequality~~.<~~ref~~>~~{{citation~~
	~~\| last1 = Erdős \| first1 = Paul \| author1-link = Paul Erdős~~
	~~\| last2 = Mordell \| first2 = L. J. \| author2-link = Louis J. Mordell~~
	~~\| last3 = Barrow \| first3 = David F. \| author3-link = David Francis Barrow~~
	~~\| issue = 4~~
	~~\| journal = [[American Mathematical Monthly]]~~
	~~\| jstor = 2300713~~
	~~\| pages = 252–254~~
	~~\| title = Solution to problem 3740~~
	~~\| volume = 44~~
	~~\| year = 1937}}.</ref> A simpler proof was later given by Mordell.~~<~~ref~~>~~{{citation~~
	~~\| last = Mordell \| first = L. J. \| author-link = Louis J. Mordell~~
	~~\| issue = 357~~
	~~\| journal = Mathematical Gazette~~
	~~\| jstor = 3614019~~
	~~\| pages = 213–215~~
	~~\| title = On geometric problems of Erdös and Oppenheim~~
	~~\| volume = 46~~
	~~\| year = 1962}}.</ref>~~

	~~== See also ==~~
	* [[Euler's theorem in geometry]]

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

	~~==External links==~~
	*[http://~~www~~.~~eleves~~.~~ens.fr/home/kortchem~~/~~olympiades~~/~~Cours~~/~~Inegalites/tin2006.pdf Hojoo Lee: Topics in Inequalities - Theorems and Techniques]~~

	~~[[Category:Triangle geometry]]~~
	~~[[Category:Geometric inequalities]~~]