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| {{unreferenced|date=August 2012}}
| | I would like to introduce myself to you, I am Jayson Simcox but I don't like when individuals use my complete title. Some time ago she selected to live in Alaska and her parents live close by. To perform lacross is one of the issues she enjoys most. Invoicing is my occupation.<br><br>my site; online psychic chat ([http://clothingcarearchworth.com/index.php?document_srl=441551&mid=customer_review Full Article]) |
| {{Expert-subject|mathematics|date=March 2011}}
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| [[File:Cubic with double point.svg|thumb|right|300px|A crunode at the origin of the curve defined by ''y''<sup>2</sup>−''x''<sup>2</sup>(''x''+1)=0]]
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| In [[mathematics]], a '''crunode''' (archaic) or '''node''' is a point where a [[curve]] intersects itself so that both branches of the curve have distinct [[tangent line]]s at the point of intersection. A crunode is also known as an ''ordinary double point''.<ref>{{cite web|last=Weisstein|first=Eric W.|title=Crunode|url=http://mathworld.wolfram.com/Crunode.html|publisher=Mathworld|accessdate=14 January 2014}}</ref>
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| For a [[plane curve]], defined as the locus of points ''f''(''x'', ''y'') = 0, where ''f''(''x'', ''y'') is a [[smooth function]] of variables ''x'' and ''y'' ranging over the real numbers, a crunode of the curve is a [[singularity theory|singularity]] of the function ''f'', where both [[partial derivative]]s <math>\partial f\over \partial x</math> and <math>\partial f\over \partial y</math> vanish. Further the [[Hessian matrix]] of second derivatives will have both positive and negative [[eigenvalues]].
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| ==See also==
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| *[[Singular point of a curve]]
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| *[[Acnode]]
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| *[[Cusp (singularity)|Cusp]]
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| *[[Tacnode]]
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| *[[Saddle point]]
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| ==References==
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| {{reflist}}
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| {{Algebraic curves navbox}}
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| [[Category:Curves]]
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| [[Category:Algebraic curves]]
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| {{differential-geometry-stub}}
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Revision as of 22:25, 11 February 2014
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