The Electronic Isograph for Roots of Polynomials
Byron O. Marshall · Journal of Applied Physics · 1950
An electronic apparatus which assists in the finding of the roots of polynomials is described. The device accepts the coefficients of polynomials of degree 10 or less and yields the absolute magnitude of the roots to a precision of 0.01 relative to the largest coefficient in the polynomial and an angular accuracy of 0.3 degree on the angle of the root. The method used is the electronic analog of the expression ω= ∑ anzn= ∑ anrn cosnθ+j ∑ anrn sinnθ.Sinnθ and cosnθ are generated by a motor-driven commutator. The radius r is controlled manually. Hence a plot of ω is placed on the oscilloscope for a fixed r as a function of θ. To find the root r is manipulated until ω crosses the origin in the ω-plane. The value of θ is found by inserting a pip on the intensity of the oscilloscope under a variable phase control. When this pip is moved to the origin of the ω-plane the phase meter indicates the angle of the root in the z plane.