百四十四角形
三次方程式の係数を求めると
2 cos  2 π 144 ⋅ 2 cos  98 π 144 + 2 cos  98 π 144 ⋅ 2 cos  94 π 144 + 2 cos  94 π 144 ⋅ 2 cos  2 π 144 = − 3 2 cos  2 π 144 ⋅ 2 cos  98 π 144 ⋅ 2 cos  94 π 144 = 2 cos  2 π 48 {\displaystyle {\begin{aligned}&2\cos {\frac {2\pi }{144}}\cdot 2\cos {\frac {98\pi }{144}}+2\cos {\frac {98\pi }{144}}\cdot 2\cos {\frac {94\pi }{144}}+2\cos {\frac {94\pi }{144}}\cdot 2\cos {\frac {2\pi }{144}}=-3\\&2\cos {\frac {2\pi }{144}}\cdot 2\cos {\frac {98\pi }{144}}\cdot 2\cos {\frac {94\pi }{144}}=2\cos {\frac {2\pi }{48}}\\\end{aligned}}}
解と係数の関係より
u 3 − 3 u − 2 cos  2 π 48 = 0 {\displaystyle u^{3}-3u-2\cos {\frac {2\pi }{48}}=0}