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There are a number of attractive polyhedron compounds consisting of five cubes. The first of these (left figures) consists of the arrangement of five cubes in the polyhedron ...

An ellipsoidal section is the curve formed by the intersection of a plane with an ellipsoid. An ellipsoidal section is always an ellipse.

Parallel lines are everywhere equidistant. This postulate is equivalent to the parallel postulate.

A singular point a for which f(z)(z-a)^n is not differentiable for any integer n>0.

In any triangle, if one of the sides is extended, the exterior angle is greater than both the interior and opposite angles.

Let f be an integer polynomial. The f can be factored into a product of two polynomials of lower degree with rational coefficients iff it can be factored into a product of ...

Hansen's problem is a problem in surveying described as follows. From the position of two known but inaccessible points A and B, determine the position of two unknown ...

An isozonohedron is a zonohedron whose faces consist of n(n-1) congruent rhombi (Fedorov 1953, pp. 256-266; Chilton and Coxeter 1963). The following table summarizes some of ...

An algebraically soluble equation of odd prime degree which is irreducible in the natural field possesses either 1. Only a single real root, or 2. All real roots.

The recurrence relation (n-1)A_(n+1)=(n^2-1)A_n+(n+1)A_(n-1)+4(-1)^n valid for n=4, 5, ... with A(2)=0 and A(3)=1 and which solves the married couples problem (Dörrie 1965, ...