三十八角形
cos  2 π 38 = 1 6 ( 1 + − 133 + 57 3 i 2 3 + − 133 − 57 3 i 2 3 3 + − 38 + ( 10 ω 2 − 3 ) − 133 + 57 3 i 2 3 + ( 10 ω + 6 ) − 133 − 57 3 i 2 3 3 3 + − 38 + ( 10 ω 2 + 6 ) − 133 + 57 3 i 2 3 + ( 10 ω − 3 ) − 133 − 57 3 i 2 3 3 3 ) {\displaystyle {\begin{aligned}\cos {\frac {2\pi }{38}}=&{\frac {1}{6}}\left({\tfrac {1+{\sqrt[{3}]{\frac {-133+57{\sqrt {3}}i}{2}}}+{\sqrt[{3}]{\frac {-133-57{\sqrt {3}}i}{2}}}}{3}}+{\sqrt[{3}]{\tfrac {-38+(10\omega ^{2}-3){\sqrt[{3}]{\frac {-133+57{\sqrt {3}}i}{2}}}+(10\omega +6){\sqrt[{3}]{\frac {-133-57{\sqrt {3}}i}{2}}}}{3}}}+{\sqrt[{3}]{\tfrac {-38+(10\omega ^{2}+6){\sqrt[{3}]{\frac {-133+57{\sqrt {3}}i}{2}}}+(10\omega -3){\sqrt[{3}]{\frac {-133-57{\sqrt {3}}i}{2}}}}{3}}}\right)\\\end{aligned}}}