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The elongated square gyrobicupola nonuniform polyhedron obtained by rotating the bottom third of a small rhombicuboctahedron (Ball and Coxeter 1987, p. 137). It is also ...

Through a point K in the plane of a triangle DeltaABC, draw parallelians through a point as illustrated above. Then there exist four points K for which ...

An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

Let X be a set of urelements, and let V(^*X) be an enlargement of the superstructure V(X). Let A in V(X) be a finitary algebra with finitely many fundamental operations. Then ...

In general, an extremal graph is the largest graph of order n which does not contain a given graph G as a subgraph (Skiena 1990, p. 143). Turán studied extremal graphs that ...

Given a number n, Fermat's factorization methods look for integers x and y such that n=x^2-y^2. Then n=(x-y)(x+y) (1) and n is factored. A modified form of this observation ...

According to Hardy and Wright (1979), the 44-digit Ferrier's prime determined to be prime using only a mechanical calculator, is the largest prime found before the days of ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...