Mathematics of paper folding - Revision history

en>Dmcq: Reverted to revision 617104574 by Begeun (talk): Illustration doesn't really show anything about the subject. (TW)

2014-10-18T15:11:19Z

Reverted to revision 617104574 by Begeun (talk): Illustration doesn't really show anything about the subject. (TW)

← Older revision		Revision as of 17:11, 18 October 2014
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en>Mama meta modal: /* External links */

2014-02-23T15:52:20Z

External links

← Older revision		Revision as of 17:52, 23 February 2014
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	~~{{About\|degeneracy~~ in ~~mathematics\|~~the ~~degeneracy of a [[Graph (mathematics)\|graph]]\|degeneracy (graph theory)\|other uses\|Degeneracy (disambiguation)}}~~		a strategy and also battle activation where you must manage your different tribe and also prevent leakages. You have so that it will build constructions which may possibly provide protection for your own personal soldiers along with the very instruction. First really focus on your protection and after its recently been taken treatment. You ought to to move forward by means of the criminal offense plan. As well as Military facilities, you also require to keep in minds the way your tribe is certainly going. For instance, collecting resources as well as widening your own tribe may be the key to good results.<br><br>
	~~{{Unreferenced\|date=December 2009}}~~

	~~In [[mathematics]],~~ a ~~'''degenerate case''' is a [[limiting case]] in which an element~~ of ~~a class of objects is qualitatively different from~~ the ~~rest~~ of the ~~class~~ and ~~hence belongs~~ to ~~another, usually simpler, class.~~ '~~''Degeneracy''' is the condition of being~~ a ~~degenerate case~~.		These amend delivers a number of notable enhancements, the alignment of which could turn out to be the new Dynasty Struggle Manner. In specific mode, you can said combating dynasties and lessen utter rewards aloft personal beat.<br><br>Pay attention to a mission's evaluation when purchasing a present. This evaluation will allow you to comprehend what age level clash of [http://mondediplo.com/spip.php?page=recherche&recherche=clans+hack clans hack] tool is perfect for and will make it known when the sport 's violent. It can help you figure out whether it is advisable to buy the sport.<br><br>In case that you are searching in support of a particular game that would buy but want to purchase it at you see, the best price possible, utilize the "shopping" tab that are available on many search motors. This will allow you to immediately equate the prices of the game at all the major retailers online. You can also see ratings for the proprietor in question, helping someone determine who you will need to buy the game because of.<br><br>If you cherished this article and you would like to obtain a lot more info with regards to hack clash of clans ([http://prometeu.net click through the next web page]) kindly go to our own website. Some sort of aboriginal phase, Alertness Day time is back your association prepares their own defenses, gathers admonition about any enemy, and starts planning extramarital liasons of confront. During this appearance there's not any attacking. Instead, there are three heavy activities during alertness day time: rearranging your showdown starting, altruistic accretion militia in your association mates, and aloof adversary warfare bases.<br><br>Our world can be influenced by supply and will need. We shall look during the the Greek-Roman model. Using special care that will highlight the role because of clash of clans hack into tool no survey within just the vast framework of which usually this provides.<br><br>Basically, it would alone acquiesce all of us to tune 2 volume zones. If you appetite for you to single added than in what kind of - as Supercell intensely acquainted t had currently all-important - you allegations assorted beeline segments. Theoretically they could create a record of alike added bulk products and solutions. If they capital to help allegation added or beneath for a couple day skip, they may well calmly familiarize 1 added segment.

	~~A degenerate case thus has special features, which depart from the properties that are~~ [~~[generic property\|generic]] in the wider class, and which would be lost under an appropriate small [[Perturbation theory\|perturbation]]~~.

	==~~In geometry==~~

	~~===Conic sections===~~
	~~{{Main\|Degenerate conic}}~~

	~~A degenerate conic is a [[conic section~~]~~] (a second-degree plane curve, the points of which satisfy an equation that~~ is ~~quadratic in one or~~ the ~~other or both variables) that fails to be an irreducible curve~~.

	* A [[Point (geometry)\|point]] is ~~a degenerate [[circle]], namely one with radius 0~~.
	* The [[line (mathematics)\|line]] is a degenerate case of a ~~[[parabola]] if~~ the ~~parabola resides~~ on ~~a [[tangent plane]]~~.
	* A [[line segment]] can be viewed as a degenerate case of an [[ellipse]] in which the [[semiminor axis]] goes to ~~zero,~~ the ~~[[Focus (geometry)\|foci]] go to~~ the ~~endpoints, and~~ the ~~[[eccentricity (mathematics)\|eccentricity]] goes to one~~.
	* An ellipse can also ~~degenerate into a single point~~.
	* A [[hyperbola]] can degenerate into two lines crossing at a ~~point, through a family~~ of ~~hyperbolae having those lines as common~~ [~~[asymptote]]s~~.

	~~===Sphere===~~

	* A [[sphere]] is a degenerate [[standard torus]] where the axis of revolution passes through the ~~center~~ of ~~the generating circle~~, ~~rather than outside it.~~

	~~===Triangle===~~

	* A degenerate [[triangle]] has [[collinear]] vertices, and ~~thus coincides with a segment covered twice~~.

	~~===Rectangle===~~
	* A segment is a degenerate case of a [[rectangle]], if this ~~has a side of length 0~~.

	* For any non-empty subset <math>S \subseteq \{1, 2, \ldots, n\}</math>, there ~~is a bounded~~, ~~axis-aligned degenerate rectangle~~

	~~:<math>R \triangleq \left\{\mathbf{x} \~~in ~~\mathbb{R}^n: x_i = c_i \ (\text{for } i\in S) \text{~~ and ~~} a_i \leq x_i \leq b_i \ (\text{for } i \notin S)\right\}~~<~~/math~~>

	~~where~~ <~~math>\mathbf{x} \triangleq [x_1, x_2, \ldots, x_n]</math~~> and ~~<math>a_i, b_i, c_i</math> are constant (with <math>a_i \leq b_i</math> for all <math>i</math>)~~. ~~The number~~ of ~~degenerate sides~~ of ~~<math>R</math> is~~ the ~~number~~ of ~~elements of the subset~~ <~~math~~>S<~~/math~~>~~. Thus~~, ~~there may be as few as one degenerate "side" or as many as <math>n</math> (in which case <math>R</math> reduces~~ to ~~a singleton point)~~.

	~~===Other===~~

	* See [[general position]] for ~~other examples.~~

	~~==Elsewhere==~~

	* A set containing a single ~~point is a degenerate [[Linear continuum\|continuum]].~~

	* A [[random variable]] which can only take one value has a [[degenerate distribution]]; its probability density is the [[Dirac Delta function]] at one point.

	* Similarly, [[root of ~~a function\|root]]s of a [[polynomial]] are said to be ''degenerate'' if they coincide, since generically the ''n'' roots of an ''n''th degree polynomial are~~ all ~~distinct. This usage carries over to eigenproblems: a degenerate [[eigenvalue]] (i.e~~. a ~~multiply coinciding root~~ of ~~the [[characteristic polynomial]]) is one that has more than one linearly independent [[eigenvector]]~~.

	* In [[quantum mechanics]] any such [[multiplicity (mathematics)\|multiplicity]] in the eigenvalues of the [[Hamiltonian operator]] gives rise to ~~[[degenerate energy level]]s. Usually any such degeneracy indicates some underlying [[symmetry]] in the system~~.

	~~== See also ==~~
	* [[Degeneracy (graph theory)]]
	* [[Degenerate form]]
	* [[Trivial (mathematics)]]
	* [[Pathological (mathematics)]]
	* [[Vacuous truth]]

	~~==External links==~~
	~~{{MathWorld\|title=Degenerate\|id=Degenerate}}~~

	~~{{DEFAULTSORT:Degeneracy (Mathematics)}}~~
	~~[[Category:Mathematical concepts]]~~

en>Mindmatrix: Reverted edits by 92.24.81.115 (talk) to last version by Monkbot

2014-01-28T23:02:02Z

Reverted edits by 92.24.81.115 (talk) to last version by Monkbot

← Older revision		Revision as of 01:02, 29 January 2014
Line 1:		Line 1:
	~~Adrianne Le~~ is the ~~name my parents gave others but you can call me anything you as~~. ~~Vermont~~ has ~~always been my home~~ and ~~I really love every day living here~~. As a ~~girl what Take into consideration like~~ is to ~~toy croquet but I would not make it my field really~~. ~~Filing gives been my profession for some time~~ and [~~http://dict~~.~~leo~~.~~org/?search~~=~~I%27m+starting I'm starting~~] ~~pretty good financially~~. ~~You can find my web property here~~: ~~http~~://~~[http:~~//~~Imageshack~~.us/~~photos~~/~~prometeu prometeu]~~.~~net~~<br><br>~~Also visit my blog post~~: ~~hack clash~~ of ~~clans -~~ [~~http://prometeu~~.~~net click through~~ the ~~next web page~~],		{{About\|degeneracy in mathematics\|the degeneracy of a [[Graph (mathematics)\|graph]]\|degeneracy (graph theory)\|other uses\|Degeneracy (disambiguation)}}
			{{Unreferenced\|date=December 2009}}

			In [[mathematics]], a '''degenerate case''' is a [[limiting case]] in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class. '''Degeneracy''' is the condition of being a degenerate case.

			A degenerate case thus has special features, which depart from the properties that are [[generic property\|generic]] in the wider class, and which would be lost under an appropriate small [[Perturbation theory\|perturbation]].

			==In geometry==

			===Conic sections===
			{{Main\|Degenerate conic}}

			A degenerate conic is a [[conic section]] (a second-degree plane curve, the points of which satisfy an equation that is quadratic in one or the other or both variables) that fails to be an irreducible curve.

			* A [[Point (geometry)\|point]] is a degenerate [[circle]], namely one with radius 0.
			* The [[line (mathematics)\|line]] is a degenerate case of a [[parabola]] if the parabola resides on a [[tangent plane]].
			* A [[line segment]] can be viewed as a degenerate case of an [[ellipse]] in which the [[semiminor axis]] goes to zero, the [[Focus (geometry)\|foci]] go to the endpoints, and the [[eccentricity (mathematics)\|eccentricity]] goes to one.
			* An ellipse can also degenerate into a single point.
			* A [[hyperbola]] can degenerate into two lines crossing at a point, through a family of hyperbolae having those lines as common [[asymptote]]s.

			===Sphere===

			* A [[sphere]] is a degenerate [[standard torus]] where the axis of revolution passes through the center of the generating circle, rather than outside it.

			===Triangle===

			* A degenerate [[triangle]] has [[collinear]] vertices, and thus coincides with a segment covered twice.

			===Rectangle===
			* A segment is a degenerate case of a [[rectangle]], if this has a side of length 0.

			* For any non-empty subset <math>S \subseteq \{1, 2, \ldots, n\}</math>, there is a bounded, axis-aligned degenerate rectangle

			:<math>R \triangleq \left\{\mathbf{x} \in \mathbb{R}^n: x_i = c_i \ (\text{for } i\in S) \text{ and } a_i \leq x_i \leq b_i \ (\text{for } i \notin S)\right\}</math>

			where <math>\mathbf{x} \triangleq [x_1, x_2, \ldots, x_n]</math> and <math>a_i, b_i, c_i</math> are constant (with <math>a_i \leq b_i</math> for all <math>i</math>). The number of degenerate sides of <math>R</math> is the number of elements of the subset <math>S</math>. Thus, there may be as few as one degenerate "side" or as many as <math>n</math> (in which case <math>R</math> reduces to a singleton point).

			===Other===

			* See [[general position]] for other examples.

			==Elsewhere==

			* A set containing a single point is a degenerate [[Linear continuum\|continuum]].

			* A [[random variable]] which can only take one value has a [[degenerate distribution]]; its probability density is the [[Dirac Delta function]] at one point.

			* Similarly, [[root of a function\|root]]s of a [[polynomial]] are said to be ''degenerate'' if they coincide, since generically the ''n'' roots of an ''n''th degree polynomial are all distinct. This usage carries over to eigenproblems: a degenerate [[eigenvalue]] (i.e. a multiply coinciding root of the [[characteristic polynomial]]) is one that has more than one linearly independent [[eigenvector]].

			* In [[quantum mechanics]] any such [[multiplicity (mathematics)\|multiplicity]] in the eigenvalues of the [[Hamiltonian operator]] gives rise to [[degenerate energy level]]s. Usually any such degeneracy indicates some underlying [[symmetry]] in the system.

			== See also ==
			* [[Degeneracy (graph theory)]]
			* [[Degenerate form]]
			* [[Trivial (mathematics)]]
			* [[Pathological (mathematics)]]
			* [[Vacuous truth]]

			==External links==
			{{MathWorld\|title=Degenerate\|id=Degenerate}}

			{{DEFAULTSORT:Degeneracy (Mathematics)}}
			[[Category:Mathematical concepts]]

en>Dmcq: /* Doubling the cube */ fix the english

2012-09-02T12:42:48Z

Doubling the cube: fix the english

New page

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