Ads
related to: singular points of a quadratic graph worksheet pdfkutasoftware.com has been visited by 10K+ users in the past month
Search results
Results from the WOW.Com Content Network
A curve with a triple point at the origin: x(t) = sin(2t) + cos(t), y(t) = sin(t) + cos(2t) In general, if all the terms of degree less than k are 0, and at least one term of degree k is not 0 in f, then curve is said to have a multiple point of order k or a k-ple point.
The singular set of x 2 = y 2 z 2 is the pair of lines given by the y and z axes. The only reasonable varieties to blow up are the origin, one of these two axes, or the whole singular set (both axes). However the whole singular set cannot be used since it is not smooth, and choosing one of the two axes breaks the symmetry between them so is not ...
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables; for example, D = 1 in the case of conic sections.
The study of the analytic structure of an algebraic curve in the neighborhood of a singular point provides accurate information of the topology of singularities. In fact, near a singular point, a real algebraic curve is the union of a finite number of branches that intersect only at the singular point and look either as a cusp or as a smooth curve.
The two families of lines on a smooth (split) quadric surface. In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine ...
This is another branch of singularity theory, based on earlier work of Hassler Whitney on critical points. Roughly speaking, a critical point of a smooth function is where the level set develops a singular point in the geometric sense. This theory deals with differentiable functions in general, rather than just polynomials.
A plane curve defined by an implicit equation (,) =,where F is a smooth function is said to be singular at a point if the Taylor series of F has order at least 2 at this point.. The reason for this is that, in differential calculus, the tangent at the point (x 0, y 0) of such a curve is defined by the equation
One could define the x-axis as a tangent at this point, but this definition can not be the same as the definition at other points. In fact, in this case, the x -axis is a "double tangent." For affine and projective varieties , the singularities are the points where the Jacobian matrix has a rank which is lower than at other points of the variety.
Ads
related to: singular points of a quadratic graph worksheet pdfkutasoftware.com has been visited by 10K+ users in the past month