Fixation index - Revision history

en>Julia W: /* FST in humans */ +wikilink

2014-07-29T01:34:22Z

FST in humans: +wikilink

← Older revision		Revision as of 03:34, 29 July 2014
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	Let me ~~first begin~~ by ~~introducing myself. home std test kit My~~ name is [http://brown.edu/Student_Services/Health_Services/Health_Education/sexual_health/sexually_transmitted_infections/hpv.php Boyd Butts] even though it is not the title on my beginning [http://Ohnotheydidnt.livejournal.com/49721712.html certification]. Playing baseball [http://www.pornextras.info/user/G49Z pornextras.info] over the counter [http://bikedance.com/blogs/post/15246 over the counter std test] std test is the pastime he will by no means stop doing. I used to be unemployed but now I am a librarian and the wage has been truly fulfilling. Puerto Rico is ~~exactly~~ where he's been ~~residing~~ for years and he will ~~never~~ move.<br><br>my ~~blog ::~~ [http://~~Riddlesandpoetry~~.~~com~~/~~?q=node~~/~~19209 std testing at home~~]		Greetings. Let me start by telling you the writer's name - Phebe. Puerto Rico is where he's been living for years and he will by no means move. One of the issues she enjoys most is to study comics and she'll be starting something else along with it. My day occupation is a meter reader.<br><br>Feel free to surf to my weblog - std testing at home ([http://chatbook.biz/blogs/post/922 Read the Full Content])

en>Andrei Marzan: Reverted to revision 591323984 by Monkbot (talk): Possible vandalism. (TW)

2014-02-15T12:02:44Z

Reverted to revision 591323984 by Monkbot (talk): Possible vandalism. (TW)

← Older revision		Revision as of 14:02, 15 February 2014
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	~~In [[geometry]], Dehn constructed two examples of planes, a '''semi-Euclidean geometry''' and a '''non-Legendrian geometry''', that have infinitely~~ ~~many lines parallel to a given one that pass through a given point, but where the sum of the angles of a triangle~~ is ~~at least π~~. ~~A similar phenomenon occurs in [[hyperbolic geometry~~]~~], except that the sum of the angles of a triangle~~ is ~~less than π. Dehn's examples use a non-Archimedean field, so that~~ the [~~[Archimedean axiom]] is violated~~. ~~They were introduced by {{harvs\|txt\|authorlink=Max Dehn\|first=Max \|last=Dehn\|year=1900}} and discussed by {{harvtxt\|Hilbert\|1902\|loc=p~~.~~127–130, or p~~. ~~42-43 in some later editions}}~~.		Let me first begin by introducing myself. home std test kit My name is [http://brown.edu/Student_Services/Health_Services/Health_Education/sexual_health/sexually_transmitted_infections/hpv.php Boyd Butts] even though it is not the title on my beginning [http://Ohnotheydidnt.livejournal.com/49721712.html certification]. Playing baseball [http://www.pornextras.info/user/G49Z pornextras.info] over the counter [http://bikedance.com/blogs/post/15246 over the counter std test] std test is the pastime he will by no means stop doing. I used to be unemployed but now I am a librarian and the wage has been truly fulfilling. Puerto Rico is exactly where he's been residing for years and he will never move.<br><br>my blog :: [http://Riddlesandpoetry.com/?q=node/19209 std testing at home]

	~~==Dehn's non-archimedean field Ω(''t'')==~~

	~~To construct his geometries, Dehn used a~~ [[Archimedean property\|non-Archimedean]] ordered [[Pythagorean field]] Ω(''t''), a [[Pythagorean closure]] of the field of rational functions '''R'''(''t''), consisting of the smallest field of real-valued rational functions containing the real constants, the identity function ''t'' (taking any real number to itself) and closed under the operation ω → √(1+ω<sup>2</~~sup>)~~. ~~The field Ω(''t'') is ordered by putting ''x''>''y'' if the function ''x'' is larger than ''y'' for sufficiently large reals~~. ~~An element ''x'' of Ω(''t'') is called '''finite''' if ''m''<''x''<''n'' for some integers ''m'',''n'', and is called '''infinite''' otherwise~~.

	~~==Dehn's semi-Euclidean geometry==~~

	~~The set of all pairs (''x'', ''y''), where ''x'' and ''y'' are any (possibly infinite) elements of~~ the ~~field Ω(''t''), and with the usual~~ [~~[metric (mathematics)\|metric]]~~

	: ~~<math>\|\|(x,y)\|\| = \sqrt{x^2+y^2}, \, <~~/~~math>~~

	~~which takes values in Ω(''t''), gives a model of [[Euclidean geometry]]~~. ~~The parallel postulate is true in this model, but if~~ the ~~deviation from the perpendicular~~ is ~~infinitesimal (meaning smaller than any positive rational number),~~ the ~~intersecting lines intersect at a point that is not in the finite part of the plane~~. ~~Hence, if the model is restricted~~ to ~~the finite part of the plane (points (''x'',''y'') with ''x''~~ and ~~''y'' finite), a geometry is obtained in which~~ the ~~parallel postulate fails but the sum of the angles of a triangle is π~~. ~~This~~ is ~~Dehn's semi-Euclidean geometry.~~

	~~==Dehn's non-Legendrian geometry==~~

	~~In the same paper, Dehn also constructed an example of a non-Legendrian geometry~~ where ~~there are infinitely many lines through a point not meeting another line, but the sum of the angles in a triangle exceeds π. Riemann~~'s ~~[[elliptic geometry]] over Ω(''t'') consists of the projective plane over Ω(''t''), which can be identified with the affine plane of points (''x'':''y'':1) together with the "line at infinity",~~ and ~~has the property that the sum of the angles of any triangle is greater than π The non-Legendrian geometry consists of the points (''x''~~:~~''y''~~:~~1) of this affine subspace such that ''tx'' and ''ty'' are finite (where as above ''t'' is the element of Ω(''t'') represented by the identity function). [~~[Saccheri–Legendre theorem\|Legendre's theorem]] states that the sum of the angles of a triangle is at most π, but assumes Archimedes's axiom, and Dehn's example shows that Legendre's theorem need not hold if Archimedes' axiom is dropped.

	~~==References==~~

	*{{Citation \| last1=Dehn \| first1=Max \| author1-link=Max Dehn \| title=Die Legendre'schen Sätze über die Winkelsumme im Dreieck \| url=http://~~books.google~~.com/~~books~~?~~id=vEbWAAAAMAAJ&pg=PA404 \| doi~~=~~10.1007~~/~~BF01448980 \| jfm=31.0471.01 \| year=1900 \| journal=[[Mathematische Annalen]] \| issn=0025-5831 \| volume=53 \| issue=3 \| pages=404–439}}~~
	*{{Citation \| last1=Hilbert \| first1=David \| author1-link=David Hilbert \| title=The foundations of geometry \| year=1902 \| publisher=The Open Court Publishing Co., La Salle, Ill. \| mr=0116216 \|url=http://www.gutenberg.org/files/17384/17384-pdf.pdf}}

	~~[[Category:Geometry]]~~
	~~[[Category:Non-Euclidean geometry]~~]

en>Monkbot: /* Estimation */Fix CS1 deprecated date parameter errors

2014-01-18T21:21:21Z

Estimation: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 23:21, 18 January 2014
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	~~Oscar~~ is ~~how he~~'s ~~known as~~ and ~~he completely enjoys this name~~. ~~North Dakota is our beginning place~~. ~~Since she was 18 she~~'s ~~been working as~~ a ~~receptionist but her marketing~~ by ~~no means arrives~~. ~~To gather badges~~ is ~~what her family~~ and ~~her appreciate~~.<br><br>~~My blog;~~ [http://~~www~~.~~revleft~~.com/vb/~~member~~.~~php?u~~=~~160656~~ www.~~revleft~~.~~com~~]		In [[geometry]], Dehn constructed two examples of planes, a '''semi-Euclidean geometry''' and a '''non-Legendrian geometry''', that have infinitely many lines parallel to a given one that pass through a given point, but where the sum of the angles of a triangle is at least π. A similar phenomenon occurs in [[hyperbolic geometry]], except that the sum of the angles of a triangle is less than π. Dehn's examples use a non-Archimedean field, so that the [[Archimedean axiom]] is violated. They were introduced by {{harvs\|txt\|authorlink=Max Dehn\|first=Max \|last=Dehn\|year=1900}} and discussed by {{harvtxt\|Hilbert\|1902\|loc=p.127–130, or p. 42-43 in some later editions}}.

			==Dehn's non-archimedean field Ω(''t'')==

			To construct his geometries, Dehn used a [[Archimedean property\|non-Archimedean]] ordered [[Pythagorean field]] Ω(''t''), a [[Pythagorean closure]] of the field of rational functions '''R'''(''t''), consisting of the smallest field of real-valued rational functions containing the real constants, the identity function ''t'' (taking any real number to itself) and closed under the operation ω → √(1+ω<sup>2</sup>). The field Ω(''t'') is ordered by putting ''x''>''y'' if the function ''x'' is larger than ''y'' for sufficiently large reals. An element ''x'' of Ω(''t'') is called '''finite''' if ''m''<''x''<''n'' for some integers ''m'',''n'', and is called '''infinite''' otherwise.

			==Dehn's semi-Euclidean geometry==

			The set of all pairs (''x'', ''y''), where ''x'' and ''y'' are any (possibly infinite) elements of the field Ω(''t''), and with the usual [[metric (mathematics)\|metric]]

			: <math>\|\|(x,y)\|\| = \sqrt{x^2+y^2}, \, </math>

			which takes values in Ω(''t''), gives a model of [[Euclidean geometry]]. The parallel postulate is true in this model, but if the deviation from the perpendicular is infinitesimal (meaning smaller than any positive rational number), the intersecting lines intersect at a point that is not in the finite part of the plane. Hence, if the model is restricted to the finite part of the plane (points (''x'',''y'') with ''x'' and ''y'' finite), a geometry is obtained in which the parallel postulate fails but the sum of the angles of a triangle is π. This is Dehn's semi-Euclidean geometry.

			==Dehn's non-Legendrian geometry==

			In the same paper, Dehn also constructed an example of a non-Legendrian geometry where there are infinitely many lines through a point not meeting another line, but the sum of the angles in a triangle exceeds π. Riemann's [[elliptic geometry]] over Ω(''t'') consists of the projective plane over Ω(''t''), which can be identified with the affine plane of points (''x'':''y'':1) together with the "line at infinity", and has the property that the sum of the angles of any triangle is greater than π The non-Legendrian geometry consists of the points (''x'':''y'':1) of this affine subspace such that ''tx'' and ''ty'' are finite (where as above ''t'' is the element of Ω(''t'') represented by the identity function). [[Saccheri–Legendre theorem\|Legendre's theorem]] states that the sum of the angles of a triangle is at most π, but assumes Archimedes's axiom, and Dehn's example shows that Legendre's theorem need not hold if Archimedes' axiom is dropped.

			==References==

			*{{Citation \| last1=Dehn \| first1=Max \| author1-link=Max Dehn \| title=Die Legendre'schen Sätze über die Winkelsumme im Dreieck \| url=http://books.google.com/books?id=vEbWAAAAMAAJ&pg=PA404 \| doi=10.1007/BF01448980 \| jfm=31.0471.01 \| year=1900 \| journal=[[Mathematische Annalen]] \| issn=0025-5831 \| volume=53 \| issue=3 \| pages=404–439}}
			*{{Citation \| last1=Hilbert \| first1=David \| author1-link=David Hilbert \| title=The foundations of geometry \| year=1902 \| publisher=The Open Court Publishing Co., La Salle, Ill. \| mr=0116216 \|url=http://www.gutenberg.org/files/17384/17384-pdf.pdf}}

			[[Category:Geometry]]
			[[Category:Non-Euclidean geometry]]

en>Phil Boswell: fixing bogus DOIs using {{cite doi}}

2012-07-17T14:30:59Z

fixing bogus DOIs using {{cite doi}}

New page

Oscar is how he's known as and he completely enjoys this name. North Dakota is our beginning place. Since she was 18 she's been working as a receptionist but her marketing by no means arrives. To gather badges is what her family and her appreciate.<br><br>My blog; [http://www.revleft.com/vb/member.php?u=160656 www.revleft.com]