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Oriented in position perpendicular to up-down, and therefore parallel to a flat surface.

A surface given by the form z=F(x,y).

The pseudosphere is the constant negative-Gaussian curvature surface of revolution generated by a tractrix about its asymptote. It is sometimes also called the tractroid, ...

The number theta in the quadric (x^2)/(a^2+theta)+(y^2)/(b^2+theta)+(z^2)/(c^2+theta)=1 is called the parameter.

A parameterization of a surface x(u,v) in u and v is regular if the tangent vectors (partialx)/(partialu) and (partialx)/(partialv) are always linearly independent.

A surface possessing a saddle point.

A 4-sphere has positive curvature, with R^2=x^2+y^2+z^2+w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)+2w=0. (2) Since r=xx^^+yy^^+zz^^ (3) dw = -(xdx+ydy+zdz)/w (4) = ...

A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices. The spherical triangle is the ...

Triangulation is the division of a surface or plane polygon into a set of triangles, usually with the restriction that each triangle side is entirely shared by two adjacent ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...