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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 ...

A one-sided surface reminiscent of the Möbius strip, attributed to Gourmalin (Bouvier and George 1979, p. 477; Boas 1995). This surface is topologically equivalent to a Klein ...

The word "order" is used in a number of different ways in mathematics. Most commonly, it refers to the number of elements in (e.g., conjugacy class order, graph order, group ...