二十六角形
平方根、立方根を用いて
x = 1 + 13 6 + 1 3 13 + 13 2 − ( 26 + 5 13 ) 2 ( 13 + 13 2 ) 3 2 + i 3 39 2 ( 13 + 13 2 ) 3 2 3 + 1 3 13 + 13 2 − ( 26 + 5 13 ) 2 ( 13 + 13 2 ) 3 2 − i 3 39 2 ( 13 + 13 2 ) 3 2 3 {\displaystyle x={\frac {1+{\sqrt {13}}}{6}}+{\frac {1}{3}}{\sqrt {\frac {13+{\sqrt {13}}}{2}}}{\sqrt[{3}]{{\frac {-(26+5{\sqrt {13}})}{2\left({\frac {13+{\sqrt {13}}}{2}}\right)^{\tfrac {3}{2}}}}+i{\frac {3{\sqrt {39}}}{2\left({\frac {13+{\sqrt {13}}}{2}}\right)^{\tfrac {3}{2}}}}}}+{\frac {1}{3}}{\sqrt {\frac {13+{\sqrt {13}}}{2}}}{\sqrt[{3}]{{\frac {-(26+5{\sqrt {13}})}{2\left({\frac {13+{\sqrt {13}}}{2}}\right)^{\tfrac {3}{2}}}}-i{\frac {3{\sqrt {39}}}{2\left({\frac {13+{\sqrt {13}}}{2}}\right)^{\tfrac {3}{2}}}}}}}
x = 1 + 13 6 + 1 3 − ( 26 + 5 13 ) 2 + i 3 39 2 3 + 1 3 − ( 26 + 5 13 ) 2 − i 3 39 2 3 {\displaystyle x={\frac {1+{\sqrt {13}}}{6}}+{\frac {1}{3}}{\sqrt[{3}]{{\frac {-(26+5{\sqrt {13}})}{2}}+i{\frac {3{\sqrt {39}}}{2}}}}+{\frac {1}{3}}{\sqrt[{3}]{{\frac {-(26+5{\sqrt {13}})}{2}}-i{\frac {3{\sqrt {39}}}{2}}}}}
cos  ( 2 π / 26 ) {\displaystyle \cos(2\pi /26)} を平方根と立方根で表すと
cos  2 π 26 = 1 + 13 12 + 1 6 − ( 26 + 5 13 ) 2 + i 3 39 2 3 + 1 6 − ( 26 + 5 13 ) 2 − i 3 39 2 3 {\displaystyle \cos {\frac {2\pi }{26}}={\frac {1+{\sqrt {13}}}{12}}+{\frac {1}{6}}{\sqrt[{3}]{{\frac {-(26+5{\sqrt {13}})}{2}}+i{\frac {3{\sqrt {39}}}{2}}}}+{\frac {1}{6}}{\sqrt[{3}]{{\frac {-(26+5{\sqrt {13}})}{2}}-i{\frac {3{\sqrt {39}}}{2}}}}}