The Apollonius Circle Problem dates to Greek antiquity, circa 250 b.c. Given three circles in the plane, find or construct a circle tangent to all three. This was generalized by replacing some circles with straight lines. Viéte [Canon mathematicus seu Ad triangula cum adpendicibus, Lutetiae:...

The Bezout–Dixon resultant method for solving systems of polynomial equations lends itself to various heuristic acceleration techniques, previously reported by the present author, which can be extraordinarily effective. In this paper we will discuss how well these techniques apply to the...

The Dixon resultant method solves a system of polynomial equations by computing its resultant. It constructs a square matrix whose determinant (det) is a multiple of the resultant (res). The naïve way to proceed is to compute det, factor it, and identify res. But often det is too large to...

In this paper we study a discrete-time growth model of the Solow type with nonconcave production function where shareholders save more than workers and the population growth dynamics is described by the logistic equation. We prove that the resulting system has a compact global attractor and we...