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crunode

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Definitions of crunode in various dictionaries:

adj - a point at which a curve crosses itself [n -S] : CRUNODAL

CRUNODE - 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 lines...

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Possible Dictionary Clues
A point where one branch of a curve crosses another branch.

Crunode description
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 lines at the point of intersection. A crunode is also known as an ordinary double point.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 of the function f, where both partial derivatives * * * * * * f * * * * x * * * * {\displaystyle \partial f \over \partial x} * and * * * * * * f * * * * y * * * * {\displaystyle \partial f \over \partial y} * vanish. Further the Hessian matrix of second derivatives will have both positive and negative eigenvalues.

Crunode description

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 lines at the point of intersection. A crunode is also known as an ordinary double point.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 of the function f, where both partial derivatives
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* {\displaystyle \partial f \over \partial x}
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* {\displaystyle \partial f \over \partial y}
* vanish. Further the Hessian matrix of second derivatives will have both positive and negative eigenvalues.

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