This project is concern with mathematical design and development of vortex based electrical machine working as motor this paper presents the vortex based mathematics used to form the rodin coil. the rodin coil is a toroidal or doughnut shaped form wound by wires in a pattern consistent with the number patterns. the windings in this coil lie on the surface of torus, but do not lie consecutively adjacent to each other. instead they reach along the surface, through the central doughnut hole area and are 30 degrees mechanically apart. due to the central circle of wires, a greatly increased magnetic field is created in the center of torus naturally, as compared to a conventional coil wound with the same amount of wire. the objective is to use the increased, coherent magnetic field produced at the center of torus to construct an electrical motor.