Search Results for ""

The bifolium is a folium with b=0. The bifolium is a quartic curve and is given by the implicit equation is (x^2+y^2)^2=4axy^2 (1) and the polar equation ...

A figure resembling a daisy or sunflower in which copies of a geometric figure of increasing size are placed at regular intervals along a spiral. The resulting figure appears ...

The term folium means "leaf" in Latin and refers and refers to a plane curve having "leaf-shaped" rounded lobes. There are a number of different sorts of folia, including ...

The quadrifolium is the 4-petalled rose curve having n=2. It has polar equation r=asin(2theta) (1) and Cartesian equation (x^2+y^2)^3=4a^2x^2y^2. (2) The area of the ...

Let C be a curve and let O be a fixed point. Let P be on C and let Q be the curvature center at P. Let P_1 be the point with P_1O a line segment parallel and of equal length ...

The "trefoil" curve is the name given by Cundy and Rollett (1989, p. 72) to the quartic plane curve given by the equation x^4+x^2y^2+y^4=x(x^2-y^2). (1) As such, it is a ...

A curve named after James Watt (1736-1819), the Scottish engineer who developed the steam engine (MacTutor Archive). The curve is produced by a linkage of rods connecting two ...

A singular point of an algebraic curve is a point where the curve has "nasty" behavior such as a cusp or a point of self-intersection (when the underlying field K is taken as ...

An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in K. A nonsingular algebraic curve is an algebraic curve ...

A general plane quartic curve is a curve of the form (1) Examples include the ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, ...