二十八角形
別の表し方として
cos  2 π 28 = 1 2 2 + 2 + 2 ⋅ cos  2 π 7 = 1 2 2 + 2 + 2 ⋅ 1 6 ( 7 ⋅ 1 + 3 3 ⋅ i 2 7 3 + 7 ⋅ 1 − 3 3 ⋅ i 2 7 3 − 1 ) {\displaystyle \cos {\frac {2\pi }{28}}={\frac {1}{2}}{\sqrt {2+{\sqrt {2+2\cdot \cos {\frac {2\pi }{7}}}}}}={\frac {1}{2}}{\sqrt {2+{\sqrt {2+2\cdot {\frac {1}{6}}\left({\sqrt {7}}\cdot {\sqrt[{3}]{\frac {1+3{\sqrt {3}}\cdot i}{2{\sqrt {7}}}}}+{\sqrt {7}}\cdot {\sqrt[{3}]{\frac {1-3{\sqrt {3}}\cdot i}{2{\sqrt {7}}}}}-1\right)}}}}}
平方根、立方根で表すと
x = 7 3 + 7 3 − 13 14 + i 3 3 14 3 + 7 3 − 13 14 − i 3 3 14 3 {\displaystyle x={\frac {\sqrt {7}}{3}}+{\frac {\sqrt {7}}{3}}{\sqrt[{3}]{{\frac {-13}{14}}+i{\frac {3{\sqrt {3}}}{14}}}}+{\frac {\sqrt {7}}{3}}{\sqrt[{3}]{{\frac {-13}{14}}-i{\frac {3{\sqrt {3}}}{14}}}}}
cos  ( 2 π / 28 ) {\displaystyle \cos(2\pi /28)} を平方根と立方根で表すと
cos  2 π 28 = 7 6 + 7 6 − 13 14 + i 3 3 14 3 + 7 6 − 13 14 − i 3 3 14 3 {\displaystyle \cos {\frac {2\pi }{28}}={\frac {\sqrt {7}}{6}}+{\frac {\sqrt {7}}{6}}{\sqrt[{3}]{{\frac {-13}{14}}+i{\frac {3{\sqrt {3}}}{14}}}}+{\frac {\sqrt {7}}{6}}{\sqrt[{3}]{{\frac {-13}{14}}-i{\frac {3{\sqrt {3}}}{14}}}}}