五十二角形
三次方程式の係数を求めると
2 cos  2 π 52 ⋅ 2 cos  18 π 52 + 2 cos  18 π 52 ⋅ 2 cos  46 π 52 + 2 cos  46 π 52 ⋅ 2 cos  2 π 52 = 2 cos  10 π 26 + 2 cos  14 π 26 + 2 cos  22 π 26 + 2 cos  4 π 13 + 2 cos  10 π 13 + 2 cos  12 π 13 = − 13 2 cos  2 π 52 ⋅ 2 cos  18 π 52 ⋅ 2 cos  46 π 52 = x 4 {\displaystyle {\begin{aligned}&2\cos {\frac {2\pi }{52}}\cdot 2\cos {\frac {18\pi }{52}}+2\cos {\frac {18\pi }{52}}\cdot 2\cos {\frac {46\pi }{52}}+2\cos {\frac {46\pi }{52}}\cdot 2\cos {\frac {2\pi }{52}}\\&=2\cos {\frac {10\pi }{26}}+2\cos {\frac {14\pi }{26}}+2\cos {\frac {22\pi }{26}}+2\cos {\frac {4\pi }{13}}+2\cos {\frac {10\pi }{13}}+2\cos {\frac {12\pi }{13}}=-{\sqrt {13}}\\&2\cos {\frac {2\pi }{52}}\cdot 2\cos {\frac {18\pi }{52}}\cdot 2\cos {\frac {46\pi }{52}}=x_{4}\\\end{aligned}}}