Eccentric pie charts and an unusual pie cutting

The eccentric pie chart, a generalization of the traditional pie chart is introduced. An arbitrary point is fixed within the circle, and rays are drawn from it. A sector is bounded by a pair of neighboring rays and the arc between them. Eccentric pie charts have the potential of visualizing multiple sets of data, especially for small numbers of items/features. The calculations of the area-proportional diagram are based on well-known equations in coordinate geometry. The resulting system of polynomial and trigonometric equations can be approximated by a fully polynomial system, once the non-polynomial functions are approximated by their Taylor series written up to the first few terms. The roots of the polynomial system have been found by the homotopy continuation method, then used as starting points of a Newton iteration for the original (non-polynomial) system. The method is illustrated on a special pie-cutting problem.