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.
We have 180 * (R-2)/R = (59/58) * 180 * (S-2)/S.
A little algebra gives RS - 118R + 116S = 0
and the factoring (R+116)*(S-118) = -116*118
It's clearer to get rid of the negative sign and write (R+116)*(118-S) = 116*118
It's obvious now that S=117 is the maximum, making R=116*118 - 116 = 13572.
Posted by xdog
on 2015-01-15 10:52:06