Talk:Crunode

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The function locus-graphed in the picture has a saddle point at the origin, so I believe its Hessian matrix must be indefinite. There exist crunodes that are local extrema of the locus function (consider ${\displaystyle f(x,y)=(x-y)^{2}(x+y)^{2}}$), so I'm not sure that there is anything to say about the Hessian here. --Tardis 16:51, 16 January 2007 (UTC)Reply

Yes you are right about the indefinite hessian. Whether (x-y)^2(x+y)^2 should be considered a crunode is an interesting question. If you take a classification of singularities, you find that x^2-y^2 and (x-y)^2(x+y)^2 have different types, the most important type being the simpler case. I'm not at all clear wherther the more complex case should really be called a curnode or not.

Taking the simplest case I think the defining characteristic is that the determinant of the hessian is negative, that is the quadratic form is hyperbolic. Acnodes have elliptics quadratic forms and cusps have parabolic forms. --Salix alba (talk) 21:26, 16 January 2007 (UTC)Reply

I've never heard the term crunode in my life. Is there a relation to node? The picture depicts what most people would call a node, not a crunode. The stuff about the Hessian contradicts the picture. This article is in serious trouble.--345Kai (talk) 07:33, 7 March 2010 (UTC)Reply

Yes the info about the Hessian was wrong, somehow it didn't get corrected last time it was pointed out. I think the term is a little dated, but it is well sourced in certain parts of the literature.--Salix (talk): 17:05, 7 March 2010 (UTC)Reply

There is a vector image available Media:Cubic_with_double_point.svg. Is it not enough?Electron Kid (talk) 23:59, 3 December 2010 (UTC)Reply