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A ruled surface is called a generalized cylinder if it can be parameterized by x(u,v)=vp+y(u), where p is a fixed point. A generalized cylinder is a regular surface wherever ...

A ruled surface is called a generalized cone if it can be parameterized by x(u,v)=p+vy(u), where p is a fixed point which can be regarded as the vertex of the cone. A ...

Let M subset R^3 be a regular surface and u_(p) a unit tangent vector to M, and let Pi(u_(p),N(p)) be the plane determined by u_(p) and the normal to the surface N(p). Then ...

A number is said to be biquadratefree (or quarticfree) if its prime factorization contains no quadrupled factors. All primes and prime powers p^n with n<=3 are therefore ...

Gauss stated the reciprocity theorem for the case n=4 x^4=q (mod p) (1) can be solved using the Gaussian integers as ...

If the Gauss map of a complete minimal surface omits a neighborhood of the sphere, then the surface is a plane. This was proven by Osserman (1959). Xavier (1981) subsequently ...

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

The distribution parameter of a noncylindrical ruled surface parameterized by x(u,v)=sigma(u)+vdelta(u), (1) where sigma is the striction curve and delta the director curve, ...

In three mutually orthogonal systems of surfaces, the lines of curvature on any surface in one of the systems are its intersections with the surfaces of the other two systems.

The Labs septic is a septic surface having 99 ordinary double points, which is the maximum number known for any septic surface.