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A subset M subset R^n is called a regular surface if for each point p in M, there exists a neighborhood V of p in R^n and a map x:U->R^n of an open set U subset R^2 onto V ...

A transformation consisting of rotations and translations which leaves a given arrangement unchanged.

The curve b(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u) is called the directrix (or base curve).

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 perimeter-bisecting line segment which originates at a vertex of a polygon. The three splitters of a triangle concur in a point known as the Nagel point Na.

A stack F on a topological space X is said to be a stack of groupoids if for each open subset U subset= X, the category F(U) is a groupoid.

The angles S_1=A_1/2 and S_2=A_2/2 obtained from solving sin(x+omega)=2sinomega (1) for x=A_1,A_2, where omega is the Brocard angle. The half-angles A_1 and A_2 are given by ...

Let M be an oriented regular surface in R^3 with normal N. Then the support function of M is the function h:M->R defined by h(p)=p·N(p).

A ruled surface M is a tangent developable of a curve y if M can be parameterized by x(u,v)=y(u)+vy^'(u). A tangent developable is a developable surface.

The planes passing through the vertices of a tetrahedron ABCD and tangent to the circumsphere at these points form another tetrahedron called the tangential tetrahedron. The ...