Computing Curves Bounding Trigonometric Planar Maps: Symbolic and Hybrid Methods

A few years ago S-H Kim investigated some problems at the boundary of number theory, optimization, and geometry. One question regarded an optimal packing of certain útriangular ovalø planar curves and another looked at some related transformations of R2 to R2 . These were investigated primarily using tools from calculus but it turns out that computational algebra methods may instead be employed to particular advantage. Moreover, generalizations that are beyond the reach of such methods are still amenable to hybrid approaches using numeric and symbolic methods in tandem. We introduce some of the specific problems and generalizations, and show by detailed example how such techniques may be implemented and deployed.