The Vincent Circle 1,2 principle may be stated as follows. If a structure is excited harmonically, the response at another position at a particular frequency will trace a circle in the complex plane as a result of a dynamic stiffness modification between two points. As either the real or imaginary part of an introduced dynamic stiffness is varied from plus and minus infinity, the structural or acoustic response will map a circle in the complex plane. This paper summarizes the basis for this little known principle. Two numerical simulations are included to demonstrate how the principle can be applied. In the first example, a cantilevered plate is used to confirm that the principle is amenable to noise problems. A similar analysis is then performed on a construction cab to illustrate the applicability of the method if the structure is excited at multiple locations. The results suggest that the principle can be used in place of or in conjunction with more sophisticated numerical optimization schemes.