Each interior angle of a regular R-gon is precisely 59/58 times that of each angle of a regular S-gon, where R ≥ S ≥ 3.

Find the largest possible value of S.

Denote by r and s number of  sides of R & S respectively. 

Since  ((r-2)/r)/((s-2)/s)=59/58      and  (s-2 )/s   approaches  1  

(s-2)/s   must be less than 58/59

58s= 59s-118   yields  s=118

therefore:

117 is the maximal integer value for S.

there was no requirement to evaluate angles for S and R .but they can be easily derived.

   

Edited on January 16, 2015, 4:49 am

Posted by Ady TZIDON on 2015-01-15 11:38:56