The central theme of this paper is the minimax approximation of a function rotated by an angle about the origin and the study of the optimal angle of rotation of least minimax error. Existence theorems indicate validity for any choice of norm. In the following formulation of the problem we will include, with obvious modifications, the cases when the function is either single-valued or multi-valued and defined on a subset of [0,1]. Computation with parameter search linear programming techniques demonstrated significant improvements often possible with the rotational procedure. While not always convergent a new algorithm was developed that proved very fast and accurate in many cases.