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A number of attractive cube 6-compounds can be constructed. A first (left figures) is obtained by combining six cubes, each rotated by 1/6 of a turn about the line joining ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

Given a reference triangle DeltaABC, the trilinear coordinates of a point P with respect to DeltaABC are an ordered triple of numbers, each of which is proportional to the ...

A method for finding recurrence relations for hypergeometric polynomials directly from the series expansions of the polynomials. The method is effective and easily ...

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

Let CD be the altitude of a triangle DeltaABC and let E be its midpoint. Then area(DeltaABC)=1/2AB·CD=AB·DE, and ABFG can be squared by rectangle squaring. The general ...

An ansatz is an assumed form for a mathematical statement that is not based on any underlying theory or principle. An example from physics is the Bethe Ansatz (Müller).

An incircle is an inscribed circle of a polygon, i.e., a circle that is tangent to each of the polygon's sides. The center I of the incircle is called the incenter, and the ...

While many computations admit shortcuts that allow them to be performed more rapidly, others cannot be sped up. Computations that cannot be sped up by means of any shortcut ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...