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The surface given by the parametric equations x = asinu (1) y = asinv (2) z = asin(u+v). (3) It is a sextic surface with algebraic equation (4) The coefficients of the first ...

A surface generated by the parametric equations x(u,v) = ucosv (1) y(u,v) = usinv (2) z(u,v) = vcosu. (3) The above image uses u in [-4,4] and v in [0,6.25]. The coefficients ...

A triple integral over three coordinates giving the volume within some region G, V=intintint_(G)dxdydz.

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The Cantor diagonal method, also called the Cantor diagonal argument or Cantor's diagonal slash, is a clever technique used by Georg Cantor to show that the integers and ...

The direct product is defined for a number of classes of algebraic objects, including sets, groups, rings, and modules. In each case, the direct product of an algebraic ...

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...

In functional analysis, the Lax-Milgram theorem is a sort of representation theorem for bounded linear functionals on a Hilbert space H. The result is of tantamount ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...