File:Abstract Math-Nonlinear Rescaling (3724051623).jpg

Roman Polyak is a leading expert on nonlinear rescaling, a mathematical approach that he developed for solving constrained optimization problems that has found use in fields ranging from structural engineering to medicine. One of the leading applications for nonlinear rescaling is the design of trusses, the complex metal frameworks that support many of the critical components of our built environment such as bridges, electrical transmission lines and radio towers. This illustration shows a mathematical plot pitting cost against the almost countless ways truss cross-beams can be arranged. The goal is to find the optimal arrangement that can be constructed at the lowest cost, while still supporting the enormous weight loads of both the equipment mounted to the truss and the truss itself. To learn more about using abstract mathematics to solve real world problems, see www.nsf.gov/discoveries/disc_summ.jsp?cntn_id=111193