282 



National Resources Planning Board 



THE ISOGRAPH 



The Isograph was developed in Bell Telephone Laboratories 

 to find mechanically the complex roots of polynomials of high 



n 



degree. Let the polynomial to be factored be p{z)='SajZ' 







n n 



or 2ojHcos7e + i2a/-'sinje if 2=r(cos9 + isine). The isograph 



i 



maps the complex values of p{z) as the variable describes the 

 circle |2|=''- This graph loops the origin once for each root 

 smaller in absolute value than r. The number of roots between 

 trial values of r is determined by counting loops, and by inter- 

 polation a value of /• is found for which the graph passes through 

 the origin. This value of r and the corresponding value of 9 

 define the real and imaginarj- parts of a root. 



Figure 88 



Courtesy Beit Teitphone Laboratories 



