216 



UNIVERSITY OF COLORADO STUDIES 



By apparent deformations of Fig. 2, illustrated by Fig. 3 and 4, it 

 is evident that the common range of z and u is a circle with as a 



center and the length 2 OA as a radius. 



27r 

 Suppose now ^ = — , where n is a positive integer and combine 



successively n equal rhombes in the same manner as OC^^D is con- 

 nected to OA2B in Fig. 2, and as it is illustrated in Fig. 5 in case 



/ 

 I 



/ 



a 



of /i,=3. Thus a closed linkage is obtained in which the vertices 

 s, 'W, u^^ • • • , ^/n-2 represent the complex numbers 



n 



z; X^O, 1, 2, 



n 



According to the general theorem it is possible to construct a 

 linkage for: 



