三百六十角形
2 cos  2 π 360 = cos  2 π 120 + i sin  2 π 120 3 + cos  2 π 120 − i sin  2 π 120 3 8 cos  2 π 360 = 64 cos  2 π 120 + i ⋅ 64 sin  2 π 120 3 + 64 cos  2 π 120 − i ⋅ 64 sin  2 π 120 3 cos  2 π 360 = 4 ( 2 ( 1 + 3 ) 5 + 5 + ( 10 − 2 ) ( 3 − 1 ) ) + 4 ( 2 ( 1 − 3 ) 5 + 5 + ( 10 − 2 ) ( 3 + 1 ) ) i 3 + 4 ( 2 ( 1 + 3 ) 5 + 5 + ( 10 − 2 ) ( 3 − 1 ) ) − 4 ( 2 ( 1 − 3 ) 5 + 5 + ( 10 − 2 ) ( 3 + 1 ) ) i 3 8 {\displaystyle {\begin{aligned}2\cos {\frac {2\pi }{360}}=&{\sqrt[{3}]{\cos {\frac {2\pi }{120}}+i\sin {\frac {2\pi }{120}}}}+{\sqrt[{3}]{\cos {\frac {2\pi }{120}}-i\sin {\frac {2\pi }{120}}}}\\8\cos {\frac {2\pi }{360}}=&{\sqrt[{3}]{64\cos {\frac {2\pi }{120}}+i\cdot 64\sin {\frac {2\pi }{120}}}}+{\sqrt[{3}]{64\cos {\frac {2\pi }{120}}-i\cdot 64\sin {\frac {2\pi }{120}}}}\\\cos {\frac {2\pi }{360}}=&{\tfrac {{\sqrt[{3}]{4\left(2\left(1+{\sqrt {3}}\right){\sqrt {5+{\sqrt {5}}}}+\left({\sqrt {10}}-{\sqrt {2}}\right)\left({\sqrt {3}}-1\right)\right)+4\left(2\left(1-{\sqrt {3}}\right){\sqrt {5+{\sqrt {5}}}}+\left({\sqrt {10}}-{\sqrt {2}}\right)\left({\sqrt {3}}+1\right)\right)i}}+{\sqrt[{3}]{4\left(2\left(1+{\sqrt {3}}\right){\sqrt {5+{\sqrt {5}}}}+\left({\sqrt {10}}-{\sqrt {2}}\right)\left({\sqrt {3}}-1\right)\right)-4\left(2\left(1-{\sqrt {3}}\right){\sqrt {5+{\sqrt {5}}}}+\left({\sqrt {10}}-{\sqrt {2}}\right)\left({\sqrt {3}}+1\right)\right)i}}}{8}}\\\end{aligned}}}