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A point p on a regular surface M in R^3 is said to be parabolic if the Gaussian curvature K(p)=0 but S(p)!=0 (where S is the shape operator), or equivalently, exactly one of ...

A parabolic cyclide formed by inversion of a ring torus when the inversion sphere is tangent to the torus.

A parabolic cyclide formed by inversion of a spindle torus when the inversion sphere is tangent to the torus.

A catastrophe which can occur for four control factors and two behavior axes. The parabolic umbilic catastrophe is given by the unfolding ...

A paracompact space is a T2-space such that every open cover has a locally finite open refinement. Paracompactness is a very common property that topological spaces satisfy. ...

Rings produced by cutting a strip that has been given m half twists and been re-attached into n equal strips (Ball and Coxeter 1987, pp. 127-128).

A set of blocks, also called a resolution class, that partition the set V, where (V,B) is a balanced incomplete block design.

A line and a plane are parallel if they do not intersect.

In the above figure, the sides a and b have the same length, appearances to the contrary. In the related illusion illustrated above, the interior lines appear to be of ...

The specification of a curve, surface, etc., by means of one or more variables which are allowed to take on values in a given specified range.