Crossed ladders problem - Revision history

en>Zgozvrm: /* Solution summary */ Clarify how equation 3 was obtained.

2014-07-31T22:13:23Z

Solution summary: Clarify how equation 3 was obtained.

← Older revision		Revision as of 00:13, 1 August 2014
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	~~Hello~~ and ~~welcome~~. ~~My title~~ is ~~Figures Wunder~~. My day ~~occupation is a meter reader. One of the extremely best things in the world for me is to do aerobics and~~ now I'~~m attempting to earn money with it~~. ~~For many years he's been residing in North Dakota and his family enjoys it~~.<br><br>my ~~webpage ::~~ [http://~~apcbook~~.com~~.ng~~/~~index.php?do=~~/~~profile~~-~~446/info/ http://apcbook.com.ng/index.php?do=/profile~~-~~446~~/~~info~~]		Myrtle Benny is how I'm called and I really feel comfy when individuals use the complete name. Playing baseball is the pastime he will never stop doing. Hiring is her working day job now but she's always wanted her personal company. California is our birth place.<br><br>Have a look at my web site at home std test, [http://change-university.com/groups/curing-your-yeast-infection-how-to-accomplish-it-easily/ find more information],

92.21.214.68: /* Solution summary */

2014-02-11T14:39:53Z

Solution summary

← Older revision		Revision as of 16:39, 11 February 2014
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	~~{{Redirect\|M-curve\|~~a ~~curve describing~~ the ~~demographics of working women\|Career woman#Limited work options}}~~		Hello and welcome. My title is Figures Wunder. My day occupation is a meter reader. One of the extremely best things in the world for me is to do aerobics and now I'm attempting to earn money with it. For many years he's been residing in North Dakota and his family enjoys it.<br><br>my webpage :: [http://apcbook.com.ng/index.php?do=/profile-446/info/ http://apcbook.com.ng/index.php?do=/profile-446/info]
	~~[[File:ECClines-3.svg\|thumb\|300px\|The [[elliptic curve]] (smooth degree 3) on~~ the ~~left~~ is ~~an M-curve, as~~ it ~~has the maximum (2) components, while the curve on the right has only 1 component~~.]]
	~~In [[real number\|real]] [[algebraic geometry]], '''Harnack~~'s ~~curve theorem''', named after [[Carl Gustav Axel Harnack\|Axel Harnack]], describes the possible numbers of [[Connected space\|connected component]]s that an algebraic curve can have,~~ in ~~terms of the degree of the curve~~. ~~For any [[algebraic curve]] of degree ''m'' in the real [[projective plane]], the number of components ''c'' is bounded by~~

	:<~~math~~>~~\frac{1-(-1)^m}{2} \le c \le \frac{(m-1)(m-2)}{2}+1.\~~ <~~/math~~>
	~~The maximum number is one more than the maximum~~ [~~[geometric genus\|genus]] of a curve of degree ''m,'' attained when the curve is nonsingular~~. ~~Moreover, any number of components in this range of possible values can be attained~~.

	~~[[File:Trott bitangents.png\|thumb\|The [[Trott curve]], shown here with 7 of its bitangents, is a quartic (degree 4) M-curve, attaining the maximum (4) components for a curve of that degree~~.]]
	~~A curve which attains the maximum number of real components is called an~~
	~~''M-curve'' (from "maximum") – for example, an [[elliptic curve]] with two components, such as <math>y^2~~=~~x^3~~-~~x,<~~/~~math> or the [[Trott curve]], a quartic with four components, are examples of M-curves.~~

	~~This theorem formed the background to [[Hilbert's sixteenth problem]].~~

	~~== References ==~~
	*D. A. Gudkov, ''The topology of real projective algebraic varieties'', Uspekhi Mat. Nauk 29 (1974), 3–79 (Russian), English transl., Russian Math. Surveys 29:~~4 (1974), 1–79~~
	*[[Carl Gustav Axel Harnack\|C. G. A. ~~Harnack]], ''Über Vieltheiligkeit der ebenen algebraischen Curven'', Math. Ann. '''10''' (1876), 189–199~~
	*G. Wilson, ''Hilbert's sixteenth problem'', Topology '''17''' (1978), 53–74

	~~[[Category:Real algebraic geometry]]~~
	~~[[Category:Theorems in algebraic geometry]~~]

en>Permafrost46: WPCleaner v1.30 - Repaired 1 link to disambiguation page - (You can help) - Closed form

2014-01-13T15:52:34Z

WPCleaner v1.30 - Repaired 1 link to disambiguation page - (You can help) - Closed form

← Older revision		Revision as of 17:52, 13 January 2014
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	The ~~writer~~ is ~~called Wilber Pegues~~. ~~Invoicing is what I do for a residing but I~~'~~ve usually wanted my personal business~~. For a ~~while I~~'~~ve been~~ in ~~Alaska but I will have to move in a yr or two~~. The ~~favorite hobby~~ for ~~him and his children~~ is ~~to perform lacross and he would never give it up.~~<br><br>~~My blog post~~: ~~phone psychic~~ [[~~http://ustanford~~.~~com/index~~.~~php?do=/profile-38218/info/ mouse click the following post~~]]		{{Redirect\|M-curve\|a curve describing the demographics of working women\|Career woman#Limited work options}}
			[[File:ECClines-3.svg\|thumb\|300px\|The [[elliptic curve]] (smooth degree 3) on the left is an M-curve, as it has the maximum (2) components, while the curve on the right has only 1 component.]]
			In [[real number\|real]] [[algebraic geometry]], '''Harnack's curve theorem''', named after [[Carl Gustav Axel Harnack\|Axel Harnack]], describes the possible numbers of [[Connected space\|connected component]]s that an algebraic curve can have, in terms of the degree of the curve. For any [[algebraic curve]] of degree ''m'' in the real [[projective plane]], the number of components ''c'' is bounded by

			:<math>\frac{1-(-1)^m}{2} \le c \le \frac{(m-1)(m-2)}{2}+1.\ </math>
			The maximum number is one more than the maximum [[geometric genus\|genus]] of a curve of degree ''m,'' attained when the curve is nonsingular. Moreover, any number of components in this range of possible values can be attained.

			[[File:Trott bitangents.png\|thumb\|The [[Trott curve]], shown here with 7 of its bitangents, is a quartic (degree 4) M-curve, attaining the maximum (4) components for a curve of that degree.]]
			A curve which attains the maximum number of real components is called an
			''M-curve'' (from "maximum") – for example, an [[elliptic curve]] with two components, such as <math>y^2=x^3-x,</math> or the [[Trott curve]], a quartic with four components, are examples of M-curves.

			This theorem formed the background to [[Hilbert's sixteenth problem]].

			== References ==
			*D. A. Gudkov, ''The topology of real projective algebraic varieties'', Uspekhi Mat. Nauk 29 (1974), 3–79 (Russian), English transl., Russian Math. Surveys 29:4 (1974), 1–79
			*[[Carl Gustav Axel Harnack\|C. G. A. Harnack]], ''Über Vieltheiligkeit der ebenen algebraischen Curven'', Math. Ann. '''10''' (1876), 189–199
			*G. Wilson, ''Hilbert's sixteenth problem'', Topology '''17''' (1978), 53–74

			[[Category:Real algebraic geometry]]
			[[Category:Theorems in algebraic geometry]]

en>WickerGuy: /* External links */ Remove duplicated link

2012-01-12T19:20:42Z

External links: Remove duplicated link

New page

The writer is called Wilber Pegues. Invoicing is what I do for a residing but I've usually wanted my personal business. For a while I've been in Alaska but I will have to move in a yr or two. The favorite hobby for him and his children is to perform lacross and he would never give it up.<br><br>My blog post: phone psychic [[http://ustanford.com/index.php?do=/profile-38218/info/ mouse click the following post]]