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There is a map from a curve to its dual, sending each point to the point dual to its tangent line. If C is algebraic then so is its dual and the degree of the dual is known as the class of the original curve. The equation of the dual of C, given in line coordinates, is known as the tangential equation of C.
The nine intersections of = and = (). In mathematics, Cramer's paradox or the Cramer–Euler paradox [1] is the statement that the number of points of intersection of two higher-order curves in the plane can be greater than the number of arbitrary points that are usually needed to define one such curve.
The first two invariants covered by the Plücker formulas are the degree d of the curve C and the degree d *, classically called the class of C. Geometrically, d is the number of times a given line intersects C with multiplicities properly counted. (This includes complex points and points at infinity since the curves are taken to be subsets of ...
Toggle Mathematics (Geometry) subsection. 1.1 Algebraic curves. 1.1.1 Rational curves. ... Space-filling curve (Peano curve) See also List of fractals by Hausdorff ...
1. The rank of a projective curve is the number of tangents to the curve meeting a generic linear subspace of codimension 2. (Semple & Roth 1949, p.84) 2. The rank of a projective surface is the rank of a curve given by the intersection of the surface with a generic hyperplane. (Semple & Roth 1949, p.193) See order, class, type. range 1.
The superellipse: a curve that lies between the ellipse and the rectangle: 1965 Oct: Pentominoes and polyominoes: five games and a sampling of problems 1965 Nov: A selection of elementary word and number problems 1965 Dec: Magic stars, graphs and polyhedrons 1966 Jan: Dr. Matrix returns, now in the guise of a neo-Freudian psychonumeranalyst ...
The dual of an isogonal (vertex-transitive) polygon is an isotoxal (edge-transitive) polygon. For example, the (isogonal) rectangle and (isotoxal) rhombus are duals. In a cyclic polygon , longer sides correspond to larger exterior angles in the dual (a tangential polygon ), and shorter sides to smaller angles.
Let X be a Riemann surface.Then the intersection number of two closed curves on X has a simple definition in terms of an integral. For every closed curve c on X (i.e., smooth function :), we can associate a differential form of compact support, the Poincaré dual of c, with the property that integrals along c can be calculated by integrals over X: