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en>Rgdboer: /* References */ Hamilton 1844

2014-12-14T03:23:04Z

References: Hamilton 1844

← Older revision		Revision as of 05:23, 14 December 2014
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	~~Hi there, I am Alyson psychic phone ([http://cartoonkorea~~.~~com/ce002/1093612 click the following website]) Pomerleau~~ and ~~I believe it sounds quite great when you say~~ it. For a whilst I've been in Alaska but I will ~~[http://www.octionx.sinfauganda.co.ug/node/22469 certified psychics]~~ have to move in a year or two. ~~Distributing manufacturing is where my main earnings arrives from and it's some thing~~ I truly ~~appreciate. The favorite pastime for him and his children is to perform lacross and he would by no means give~~ it up.<br><br>~~Look at~~ my ~~web-site~~ ... [http://www.~~edmposts~~.~~com~~/~~build~~-a-~~beautiful~~-organic-garden~~-using-these-ideas/ tarot card readings~~]		The individual who wrote the article is known as Jayson Hirano and he totally digs that title. He is an purchase clerk and it's something he really enjoy. For a whilst I've been in Alaska but I will have to move in a year or two. I am truly fond of handwriting but I can't make it my profession truly.<br><br>Feel free to visit my webpage ... [http://www.prograd.uff.br/novo/facts-about-growing-greater-organic-garden spirit messages]

en>Yobot: WP:CHECKWIKI error fixes + other fixes using AWB (9930)

2014-02-10T11:36:42Z

WP:CHECKWIKI error fixes + other fixes using AWB (9930)

← Older revision		Revision as of 13:36, 10 February 2014
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	~~In [[mathematics]]~~, ~~'''Proizvolov's identity''' is an identity concerning sums of differences of~~ [~~[positive integer~~]]s. ~~The identity was posed by Vyacheslav Proizvolov as~~ a ~~problem~~ in ~~the 1985 All-Union~~ [~~[Soviet Student Olympiads]] {{harv\|Savchev\|Andreescu\|2002\|p=66}}.~~		Hi there, I am Alyson psychic phone ([http://cartoonkorea.com/ce002/1093612 click the following website]) Pomerleau and I believe it sounds quite great when you say it. For a whilst I've been in Alaska but I will [http://www.octionx.sinfauganda.co.ug/node/22469 certified psychics] have to move in a year or two. Distributing manufacturing is where my main earnings arrives from and it's some thing I truly appreciate. The favorite pastime for him and his children is to perform lacross and he would by no means give it up.<br><br>Look at my web-site ... [http://www.edmposts.com/build-a-beautiful-organic-garden-using-these-ideas/ tarot card readings]

	~~To state the identity, take the first 2''N'' positive integers,~~

	:~~1, 2, 3,~~ ...~~, 2''N'' − 1, 2''N'',~~

	~~and partition them into two subsets of ''N'' numbers each. Arrange one subset in increasing order:~~

	~~:<math> A_1 < A_2 < \cdots < A_N. </math>~~

	~~Arrange the other subset in decreasing order:~~

	~~:<math> B_1 > B_2 > \cdots > B_N~~. </~~math>~~

	~~Then the sum~~

	~~:<math> \|A_1-B_1\| + \|A_2-B_2\| + \cdots + \|A_N-B_N\| <~~/~~math>~~

	~~is always equal~~ to ~~''N''<sup>2</sup>~~.

	~~==Example==~~
	~~Take for example~~ '~~'N'' = 3~~. The ~~set of numbers~~ is ~~then {1, 2, 3, 4, 5, 6}. Select three numbers of this set, say 2, 3~~ and 5. ~~Then the sequences ''A'' and ''B'' are:~~
	~~:''A''~~<~~sub~~>1<~~/sub~~> ~~= 2, ''A''<sub>2</sub> = 3, and ''A''<sub>''3''</sub> = 5;~~
	~~:''B''<sub>1</sub> = 6, ''B''<sub>2</sub> = 4, and ''B''<sub>''3''</sub> = 1~~.

	~~The sum is~~
	~~:<math>\|A_1-B_1\| + \|A_2-B_2\| + \|A_3-B_3\| = \|2-6\| + \|3-4\| + \|5-1\| = 4+1+4 = 9, </math>~~
	~~which indeed equals 3<sup>2</sup>~~.

	~~==References==~~
	* {{Citation \| last = Savchev \| first = Svetoslav \| last2 = Andreescu \| first2 = Titu \| year = 2002 \| title = Mathematical miniatures \| volume = 43 \| series = Anneli Lax New Mathematical Library \| publisher = Mathematical Association of America \| isbn = 0-88385-645-X}}.

	~~==External links==~~
	*[http://www.~~cut~~-~~the~~-~~knot.org/Curriculum/Games/ProizvolovGame.shtml Proizvolov's identity] at cut~~-~~the~~-~~knot.org~~

	~~[[Category:Recreational mathematics]]~~
	~~[[Category:Theorems in number theory]~~]

en>Incnis Mrsi: tweaks and fixes

2014-01-31T15:21:04Z

tweaks and fixes

← Older revision		Revision as of 17:21, 31 January 2014
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	~~I would like to introduce myself to you~~, ~~I am Jayson Simcox but I don~~'~~t like when people use my full name~~. ~~Distributing manufacturing is how he makes~~ a ~~living~~. ~~Her family lives~~ in ~~Ohio~~. The ~~preferred pastime for him and his children~~ is ~~to play lacross~~ and ~~he would by no means give it up~~.<br><br>~~Also visit my blog~~ ... ~~clairvoyant psychic (~~[http://~~modenpeople~~.co.kr/~~modn~~/~~qna~~/~~292291 modenpeople~~.co.kr])		In [[mathematics]], '''Proizvolov's identity''' is an identity concerning sums of differences of [[positive integer]]s. The identity was posed by Vyacheslav Proizvolov as a problem in the 1985 All-Union [[Soviet Student Olympiads]] {{harv\|Savchev\|Andreescu\|2002\|p=66}}.

			To state the identity, take the first 2''N'' positive integers,

			:1, 2, 3, ..., 2''N'' − 1, 2''N'',

			and partition them into two subsets of ''N'' numbers each. Arrange one subset in increasing order:

			:<math> A_1 < A_2 < \cdots < A_N. </math>

			Arrange the other subset in decreasing order:

			:<math> B_1 > B_2 > \cdots > B_N. </math>

			Then the sum

			:<math> \|A_1-B_1\| + \|A_2-B_2\| + \cdots + \|A_N-B_N\| </math>

			is always equal to ''N''<sup>2</sup>.

			==Example==
			Take for example ''N'' = 3. The set of numbers is then {1, 2, 3, 4, 5, 6}. Select three numbers of this set, say 2, 3 and 5. Then the sequences ''A'' and ''B'' are:
			:''A''<sub>1</sub> = 2, ''A''<sub>2</sub> = 3, and ''A''<sub>''3''</sub> = 5;
			:''B''<sub>1</sub> = 6, ''B''<sub>2</sub> = 4, and ''B''<sub>''3''</sub> = 1.

			The sum is
			:<math>\|A_1-B_1\| + \|A_2-B_2\| + \|A_3-B_3\| = \|2-6\| + \|3-4\| + \|5-1\| = 4+1+4 = 9, </math>
			which indeed equals 3<sup>2</sup>.

			==References==
			* {{Citation \| last = Savchev \| first = Svetoslav \| last2 = Andreescu \| first2 = Titu \| year = 2002 \| title = Mathematical miniatures \| volume = 43 \| series = Anneli Lax New Mathematical Library \| publisher = Mathematical Association of America \| isbn = 0-88385-645-X}}.

			==External links==
			*[http://www.cut-the-knot.org/Curriculum/Games/ProizvolovGame.shtml Proizvolov's identity] at cut-the-knot.org

			[[Category:Recreational mathematics]]
			[[Category:Theorems in number theory]]

en>Quondum: /* lead */ added mention of use for rotation

2012-05-02T09:47:42Z

lead: added mention of use for rotation

New page

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