2607:F470:6:3003:3087:39AF:47F4:CB6: /* Robust fuzzy extractors */

2014-11-23T21:53:51Z

Robust fuzzy extractors

← Older revision		Revision as of 23:53, 23 November 2014
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	~~[[File:Harcourt theorem.svg\|right\|400px]]~~

	'''Harcourt's theorem''' is a formula in [[geometry]] for the [[area]] of a [[triangle]], as a function of its side lengths and the perpendicular distances of its vertices from an arbitrary line.<ref>{{citation
	~~\| last1 = Dergiades \| first1 = Nikolaos~~
	~~\| last2 = Salazar \| first2 = Juan Carlos~~
	~~\| journal = Forum Geometricorum~~
	~~\| mr = 2004117~~
	~~\| pages = 117–124~~
	~~\| title = Harcourt's theorem~~
	~~\| url = http://forumgeom.fau.edu/FG2003volume3/FG200313.pdf~~
	~~\| volume = 3~~
	~~\| year = 2003}}.</ref>~~

	~~The theorem~~ is ~~named after J~~. ~~Harcourt~~, an ~~Irish professor~~.<~~ref~~>~~{{citation\|title=Exercises de géométrie: comprenant l~~'~~exposé des méthodes géométriques et 2000 questions résolues\|series=Cours de mathématiques elementaires\|first=F.\|last=G~~.-~~M.\|edition=5th\|publisher=Maison A. Mame et fils (Tours) & J. de Gigord (Paris)\|year=1912\|page=750\|url=~~http://~~quod~~.~~lib~~.~~umich.edu~~/u/~~umhistmath~~/~~ACV3924~~.~~0001~~.~~001/780\|contribution=Théorème de Harcourt\|language=French}}~~.<~~/ref~~>		When compared to many life insurance quotation companies, My Term Life Insurance offers information about the coverage in three separate locations: term life insurance, critical illness insurance, and mortgage protection. Payroll deductions are dollar values taken from the gross salary of an employee; they can be either mandatory or voluntary. There are many different types of term insurance and very many reasons why people buy these policies. 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	~~==Statement==~~
	~~Let~~ a ~~[[triangle]] be given with [[vertex (geometry)\|vertices]] ''A''~~, ~~''B''~~, ~~and ''C''~~, ~~opposite sides of lengths ''~~a'', ~~''b''~~, and '~~'c''~~, ~~area ''K''~~, and a ~~line~~ that is ~~[[tangent]]~~ to the ~~triangle's [[incircle]]~~ at ~~any point on~~ that ~~circle~~. ~~Denote~~ the ~~signed perpendicular distances~~ of the ~~vertices from the line~~ as ''a''<~~sub~~>1</~~sub>~~, ~~''b''<sub>1</sub>~~, and ~~''c''~~<~~sub~~>1<~~/sub~~>, ~~with~~ a ~~distance being negative if and only if~~ the ~~vertex is~~ on the ~~opposite side~~ of ~~the line from the incenter~~. ~~Then~~

	~~:<math>a a_1 + b b_1 + c c_1 = 2K~~.</~~math>~~

	==~~Degenerate case==~~
	If the ~~tangent line contains one of~~ the ~~sides~~ of the ~~triangle, then two of the distances are zero and the formula collapses~~ to the ~~familiar formula~~ that ~~twice the area of~~ a ~~triangle~~ is ~~a base (the coinciding triangle side) times the altitude from that base~~.

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

	~~[[Category:Circles]]~~
	~~[[Category:Triangle geometry]]~~

en>AnomieBOT: Dating maintenance tags: {{Technical}}

2014-01-06T02:46:44Z

Dating maintenance tags: {{Technical}}

← Older revision		Revision as of 04:46, 6 January 2014
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	~~Tobias is what~~'s ~~written on my start certificate and I thoroughly dig that name. Hawaii~~ is ~~where by me and my spouse reside. 1~~ of ~~the issues I adore most is drawing and now I am trying to get paid income with it. Procuring has been my working day position for~~ a ~~whilst~~ and the ~~salary has been really satisfying~~. I'~~ve been doing the job on my website for some time now. Test it out below:~~ http://~~www~~.~~agrupacionmusicalalbeniz~~.~~com~~/~~cgi-bin~~/~~comprar~~/[http://~~Mondediplo~~.~~com~~/~~spip~~.~~php?page~~=~~recherche&recherche~~=~~slip-calvin-klein~~.~~php slip-calvin-klein~~.~~php]~~<br><br>~~Look into my web blog - [http:~~//~~www~~.~~agrupacionmusicalalbeniz~~.~~com~~/~~cgi-bin/comprar/slip-calvin-klein~~.~~php slip Calvin Klein~~]		[[File:Harcourt theorem.svg\|right\|400px]]

			'''Harcourt's theorem''' is a formula in [[geometry]] for the [[area]] of a [[triangle]], as a function of its side lengths and the perpendicular distances of its vertices from an arbitrary line.<ref>{{citation
			\| last1 = Dergiades \| first1 = Nikolaos
			\| last2 = Salazar \| first2 = Juan Carlos
			\| journal = Forum Geometricorum
			\| mr = 2004117
			\| pages = 117–124
			\| title = Harcourt's theorem
			\| url = http://forumgeom.fau.edu/FG2003volume3/FG200313.pdf
			\| volume = 3
			\| year = 2003}}.</ref>

			The theorem is named after J. Harcourt, an Irish professor.<ref>{{citation\|title=Exercises de géométrie: comprenant l'exposé des méthodes géométriques et 2000 questions résolues\|series=Cours de mathématiques elementaires\|first=F.\|last=G.-M.\|edition=5th\|publisher=Maison A. Mame et fils (Tours) & J. de Gigord (Paris)\|year=1912\|page=750\|url=http://quod.lib.umich.edu/u/umhistmath/ACV3924.0001.001/780\|contribution=Théorème de Harcourt\|language=French}}.</ref>

			==Statement==
			Let a [[triangle]] be given with [[vertex (geometry)\|vertices]] ''A'', ''B'', and ''C'', opposite sides of lengths ''a'', ''b'', and ''c'', area ''K'', and a line that is [[tangent]] to the triangle's [[incircle]] at any point on that circle. Denote the signed perpendicular distances of the vertices from the line as ''a''<sub>1</sub>, ''b''<sub>1</sub>, and ''c''<sub>1</sub>, with a distance being negative if and only if the vertex is on the opposite side of the line from the incenter. Then

			:<math>a a_1 + b b_1 + c c_1 = 2K.</math>

			==Degenerate case==
			If the tangent line contains one of the sides of the triangle, then two of the distances are zero and the formula collapses to the familiar formula that twice the area of a triangle is a base (the coinciding triangle side) times the altitude from that base.

			==References==
			{{reflist}}

			[[Category:Circles]]
			[[Category:Triangle geometry]]

en>John of Reading: Typo and General fixing, replaced: the the → the, typos fixed: , → , (2) using AWB

2012-05-21T12:53:25Z

Typo and General fixing, replaced: the the → the, typos fixed: , → , (2) using AWB

New page

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Fuzzy extractor - Revision history

2607:F470:6:3003:3087:39AF:47F4:CB6: /* Robust fuzzy extractors */

en>AnomieBOT: Dating maintenance tags: {{Technical}}

en>John of Reading: Typo and General fixing, replaced: the the → the, typos fixed: , → , (2) using AWB