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A set of quadratic surfaces which share foci. Ellipsoids and one- and two-sheeted hyperboloids can be confocal. These three types of surfaces can be combined to form an ...

A plot of equipotential curves. If desired, the regions between contours can be shaded or colored to indicate their magnitude. Contour plots are implemented in the Wolfram ...

A curve whose name means skull-like. It is given by the polar equation r=asint+bsqrt(1-pcos^2t)+csqrt(1-qcos^2t), where a,b,c>0, a<b+c, 0<p<1, 0<q<1, and p!=q. The top of the ...

The inner and outer spheres tangent internally to a cone and also to a plane intersecting the cone are called Dandelin spheres. The spheres can be used to show that the ...

The operation of drilling a tubular neighborhood of a knot K in S^3 and then gluing in a solid torus so that its meridian curve goes to a (p,q)-curve on the torus boundary of ...

The ding-dong surface is the cubic surface of revolution given by the equation x^2+y^2=(1-z)z^2 (1) (Hauser 2003) that is closely related to the kiss surface. The surface can ...

A point traced out twice as a closed curve is traversed. The maximum number of double points for a nondegenerate quartic curve is three. An ordinary double point is also ...

The Dürer folium is a special case of the rose curve with n=1. It is therefore also an epitrochoid. It has polar equation r=asin(theta/2) (1) and can be written as a ...

The surface of revolution given by the parametric equations x(u,v) = cosusin(2v) (1) y(u,v) = sinusin(2v) (2) z(u,v) = sinv (3) for u in [0,2pi) and v in [-pi/2,pi/2]. It is ...

Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...