Each interior angle of a regular Rgon is precisely 59/58 times that of each angle of a regular Sgon, where R ≥ S ≥ 3.
Find the largest possible value of S.
We have 180 * (R2)/R = (59/58) * 180 * (S2)/S.
A little algebra gives RS  118R + 116S = 0
and the factoring (R+116)*(S118) = 116*118
It's clearer to get rid of the negative sign and write (R+116)*(118S) = 116*118
It's obvious now that S=117 is the maximum, making R=116*118  116 = 13572.

Posted by xdog
on 20150115 10:52:06 