The computational potential of rational approximations

This article treats the subject of rational approximations as a typical subject for a mathematical laboratory. Following a brief description of such a laboratory, equipped with a set of micro-computers, rational approximations are introduced via two typical significant examples, using only very rudimentary calculus. Pedagogical considerations guided the choice of material, style, and level of presentation, while emphasizing the learning process in a mathematical laboratory environment. Using interpolative techniques, approximations with nearly equal-ripple errors are constructed. The advantage of rational over polynomial approximations-when more than two parameters are involved-is demonstrated, revealing the computational potential of rational approximations.