A Novel Type of Isograph (Algebraic Equation Solver)

Polynomial equations occur quite often in physical and mathematical problems and require an exact solution. Several problems in control engineering, aerodynamics, and many other fields require the formulation and exact solution of algebraic equations of quite a high order. In the past, several mechanical and electrical machines for the determination of the roots of polynomials have been developed, but all of them suffer from the serious disadvantage that they are very expensive and are incapable of high accuracy and rapidity of operation. This paper describes the development, design, and construction of an inexpensive and portable isograph which is capable of locating the roots of a polynomial with fairly high accuracy. This isograph can serve as a valuable aid to large-scale computing machinery, for which the roots of a polynomial must be isolated before further calculations can be performed. It can also serve as a very useful adjunct to other mathematical processes such as complementary solution of differential equations, determination of latent roots of a matrix, and similar other applications. It is hoped that this inexpensive and portable instrument will prove extremely useful in the design of servosystems and in other fields where the problem may be presented as a polynomial and that theoretical studies of engineering problems will be greatly augmented by its use.