rational curve

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• Rational normal curve — In mathematics, the rational normal curve is a smooth, rational curve C of degree n in projective n space mathbb{P}^n. It is a simple example of a projective variety. The twisted cubic is the special case of n =3.DefinitionThe rational normal… …   Wikipedia

• Curve — (v. lat., Math.), krumme Linie (vgl. Linie). Man unterscheidet ebene Curven od. Curven einfacher Krümmung, welche ganz in einer Ebene liegen, z.B. der Kreis, u. Curven doppelter Krümmung, von denen kein noch so kleiner Theil in einer Ebene liegt …   Pierer's Universal-Lexikon

• Rational surface — In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two. Rational surfaces are the simplest of the 10 or so classes of… …   Wikipedia

• Rational motion — In kinematics, the motion of a rigid body is defined as a continuous set of displacements. One parameter motions can be definedas a continuous displacement of moving object with respect to a fixed frame in Euclidean three space ( E 3), where the… …   Wikipedia

• Rational number — In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. The set of all… …   Wikipedia

• Rational variety — In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to projective space of some dimension over K. This is a question on its function field: is it up to isomorphism the field of all… …   Wikipedia

• Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… …   Wikipedia

• Inverse curve — In geometry, the inverse curve of a given curve C with respect to a fixed circle with center O and radius a is the locus of points P for which OPQ are collinear and OP • PQ = a 2 as Q runs over the original curve C .We may invert a plane… …   Wikipedia

• Bow curve — A bow curve is a quartic plane curve with the equation::x^4=x^2y y^3. ,The bow curve has a single triple point at x=0, y=0, and consequently is a rational curve, with genus zero. Expanding around zero, the three branches have series y 1 =… …   Wikipedia

• Bullet-nose curve — In mathematics, a bullet nose curve is a unicursal quartic curve with three inflection points, given by the equation:a^2y^2 b^2x^2=x^2y^2 ,The bullet curve has three double points in the real projective plane, at x=0 and y=0, x=0 and z=0, and y=0 …   Wikipedia

• Non-uniform rational B-spline — Three dimensional NURBS surfaces can have complex, organic shapes. Control points influence the directions the surface takes. The outermost square below delineates the X/Y extents of the surface …   Wikipedia