三十五角形
cos  2 π 35 = cos  ( π 5 − π 7 ) = cos  π 5 cos  π 7 + sin  π 5 sin  π 7 = 1 4 ( 5 + 1 ) ⋅ cos  π 7 + 1 4 ( 10 − 2 5 ) ⋅ sin  π 7 = 5 + 1 4 ⋅ 3 ( 20 + 2 28 − 84 i 3 3 + 2 28 + 84 i 3 3 ) 12 + 10 − 2 5 4 ⋅ 3 ( 28 − 2 28 − 84 i 3 3 − 2 28 + 84 i 3 3 ) 12 {\displaystyle {\begin{aligned}\cos {\frac {2\pi }{35}}=&\cos \left({\frac {\pi }{5}}-{\frac {\pi }{7}}\right)\\=&\cos {\frac {\pi }{5}}\cos {\frac {\pi }{7}}+\sin {\frac {\pi }{5}}\sin {\frac {\pi }{7}}\\=&{\frac {1}{4}}\left({\sqrt {5}}+1\right)\cdot \cos {\frac {\pi }{7}}+{\frac {1}{4}}\left({\sqrt {10-2{\sqrt {5}}}}\right)\cdot \sin {\frac {\pi }{7}}\\=&{\frac {{\sqrt {5}}+1}{4}}\cdot {\frac {\sqrt {3\left(20+2{\sqrt[{3}]{28-84i{\sqrt {3}}}}+2{\sqrt[{3}]{28+84i{\sqrt {3}}}}\right)}}{12}}+{\frac {\sqrt {10-2{\sqrt {5}}}}{4}}\cdot {\frac {\sqrt {3\left(28-2{\sqrt[{3}]{28-84i{\sqrt {3}}}}-2{\sqrt[{3}]{28+84i{\sqrt {3}}}}\right)}}{12}}\end{aligned}}}
よって