Plane curve — In mathematics, a plane curve is a curve in a Euclidean plane (cf. space curve). The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. A smooth plane curve is a curve in a … 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
Trott curve — In real algebraic geometry, the Trott curve is the set of points ( x , y ) satisfying the degree four polynomial equation:displaystyle 144(x^4+y^4) 225(x^2+y^2)+350x^2y^2+81=0.These points form a nonsingular quartic plane curve that has genus… … Wikipedia
Bean curve — The bean curve is a quartic plane curve with the equation::x^4+x^2y^2+y^4=x(x^2+y^2) ,It is not the same as another curve also called the bean curve, or crooked egg curve, but both curves belong to a family of similar bean shaped curves.The bean… … Wikipedia
Cruciform curve — The cruciform curve, or cross curve is a quartic plane curve given by the equation Cruciform with parameters (b,a) being (1,1) in red; (2,2) in green; (3,3) in blue … Wikipedia
Ampersand curve — In mathematics, the ampersand curve is a quartic plane curve given by the equation:: (y^2 x^2)(x 1)(2x 3)=4(x^2+y^2 2x)^2.It is an algebraic curve of genus zero, with three ordinary double points, all in the real plane. By the Plücker formulas,… … 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
Bicuspid curve — The biscuspid is a quartic plane curve with the equation:(x^2 a^2)(x a)^2+(y^2 a^2)^2=0 ,where a determines the size of the curve.The bicuspid has only the two nodes as singularities, and hence is a curve of genus one, with j invariant −4096/11.… … Wikipedia
Swastika curve — The swastika curve is the name given by Cundy and Rollett to the quartic plane curve with the Cartesian equation: y^4 x^4 = xy,, or, equivalently, the polar equation:r^2 = an(2 heta)/2. ,The curve looks similar to the right handed swastika, but… … Wikipedia
Bézier curve — Cubic Bézier curve A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case. In… … Wikipedia
