百八十角形
三次方程式の係数を求めると
cos  ( 2 π / 180 ) {\displaystyle \cos(2\pi /180)} を平方根と立方根で表すと
cos  2 π 180 = 1 4 10 − 20 + 3 + 15 + ( 30 − 180 − 5 − 1 ) i 3 + 1 4 10 − 20 + 3 + 15 − ( 30 − 180 − 5 − 1 ) i 3 {\displaystyle \cos {\frac {2\pi }{180}}={\frac {1}{4}}{\sqrt[{3}]{{\sqrt {10-{\sqrt {20}}}}+{\sqrt {3}}+{\sqrt {15}}+\left({\sqrt {30-{\sqrt {180}}}}-{\sqrt {5}}-1\right)i}}+{\frac {1}{4}}{\sqrt[{3}]{{\sqrt {10-{\sqrt {20}}}}+{\sqrt {3}}+{\sqrt {15}}-\left({\sqrt {30-{\sqrt {180}}}}-{\sqrt {5}}-1\right)i}}}