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The surface which is the inverse of the ellipsoid in the sense that it "goes in" where the ellipsoid "goes out." It is given by the parametric equations x = acos^3ucos^3v (1) ...

Given a regular surface M, an asymptotic curve is formally defined as a curve x(t) on M such that the normal curvature is 0 in the direction x^'(t) for all t in the domain of ...

A parametric latitude which gives a sphere equal surface area relative to an ellipsoid. The authalic latitude is defined by beta=sin^(-1)(q/(q_p)), (1) where ...

An identity in calculus of variations discovered in 1868 by Beltrami. The Euler-Lagrange differential equation is (partialf)/(partialy)-d/(dx)((partialf)/(partialy_x))=0. (1) ...

B^^ = T^^xN^^ (1) = (r^'xr^(''))/(|r^'xr^('')|), (2) where the unit tangent vector T and unit "principal" normal vector N are defined by T^^ = (r^'(s))/(|r^'(s)|) (3) N^^ = ...

There are three types of boundary conditions commonly encountered in the solution of partial differential equations: 1. Dirichlet boundary conditions specify the value of the ...

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 ...