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A conical wedge is an ungula obtained by cutting a solid cone with a plane placed at an angle oblique to its base. For the special conical wedge obtained from a cone of ...

Two sextuples of skew lines on the general cubic surface such that each line of one is skew to one line in the other set. In all, there are 30 points, with two lines through ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...

The elliptic hyperboloid is the generalization of the hyperboloid to three distinct semimajor axes. The elliptic hyperboloid of one sheet is a ruled surface and has Cartesian ...

A quadratic surface which has elliptical cross section. The elliptic paraboloid of height h, semimajor axis a, and semiminor axis b can be specified parametrically by x = ...

The Enneper surfaces are a three-parameter family of surfaces with constant negative curvature (and nonconstant mean curvature). In general, they are described by elliptic ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the first fundamental form is the inner product of tangent vectors, ...

The hyperbolic cylinder is a quadratic surface given by the equation (x^2)/(a^2)-(y^2)/(b^2)=-1. (1) It is a ruled surface. It can be given parametrically by x = asinhu (2) y ...

The partial differential equation (1+f_y^2)f_(xx)-2f_xf_yf_(xy)+(1+f_x^2)f_(yy)=0 (Gray 1997, p. 399), whose solutions are called minimal surfaces. This corresponds to the ...

A path, also known as a rhumb line, which cuts a meridian on a given surface at any constant angle but a right angle. If the surface is a sphere, the loxodrome is a spherical ...