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A prismatoid having planar sides and the same number of vertices in both of its parallel planes. The faces of a prismoid are therefore either trapezoids or parallelograms. ...

If a line intersects one of two parallel lines, both of which are coplanar with the original line, then it must intersect the other also. This axiom is equivalent to the ...

Given a vector space V, its projectivization P(V), sometimes written P(V-0), is the set of equivalence classes x∼lambdax for any lambda!=0 in V-0. For example, complex ...

The evolute of the prolate cycloid x = at-bsint (1) y = a-bcost (2) (with b>a) is given by x = a[t+((bcost-a)sint)/(acost-b)] (3) y = (a(a-bcost)^2)/(b(acost-b)). (4)

A map projection in which the parallels are represented by concentric circular arcs and the meridians by concurrent curves.

A projection in which latitude lines are parallel but meridians are curves.

For a quadrilateral which is not cyclic, Ptolemy's theorem becomes an inequality: AB×CD+BC×DA>AC×BD. The Ptolemy inequality is still valid when ABCD is a triangular pyramid ...

A pyritohedron is an irregular dodecahedron composed of identical irregular pentagons. The name "pyritohedron" derives from that fact that a common crystal form in pyrite has ...

One of the four regions of the plane defined by the four possible combinations of signs (+,+), (+,-), (-,+), and (-,-) for (x,y).

A flexible polyhedron due to C. Schwabe (with the appearance of having four horns) which flexes from one totally flat configuration to another, passing through intermediate ...