Superlens: Difference between revisions

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{{unreferenced|date=August 2012}}
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{{Expert-subject|mathematics|date=March 2011}}
[[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]]
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>
 
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]].
 
==See also==
*[[Singular point of a curve]]
*[[Acnode]]
*[[Cusp (singularity)|Cusp]]
*[[Tacnode]]
*[[Saddle point]]
 
==References==
{{reflist}}
 
{{Algebraic curves navbox}}
 
[[Category:Curves]]
[[Category:Algebraic curves]]
 
 
{{differential-geometry-stub}}

Latest revision as of 05:29, 10 December 2014

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