四十一角形
2 cos  2 π 41 + 2 cos  18 π 41 + 2 cos  6 π 41 + 2 cos  28 π 41 = x 1 2 cos  4 π 41 + 2 cos  36 π 41 + 2 cos  12 π 41 + 2 cos  26 π 41 = x 2 2 cos  8 π 41 + 2 cos  10 π 41 + 2 cos  24 π 41 + 2 cos  30 π 41 = x 3 2 cos  16 π 41 + 2 cos  20 π 41 + 2 cos  22 π 41 + 2 cos  34 π 41 = x 4 2 cos  32 π 41 + 2 cos  40 π 41 + 2 cos  14 π 41 + 2 cos  38 π 41 = x 5 {\displaystyle {\begin{aligned}&2\cos {\frac {2\pi }{41}}+2\cos {\frac {18\pi }{41}}+2\cos {\frac {6\pi }{41}}+2\cos {\frac {28\pi }{41}}=x_{1}\\&2\cos {\frac {4\pi }{41}}+2\cos {\frac {36\pi }{41}}+2\cos {\frac {12\pi }{41}}+2\cos {\frac {26\pi }{41}}=x_{2}\\&2\cos {\frac {8\pi }{41}}+2\cos {\frac {10\pi }{41}}+2\cos {\frac {24\pi }{41}}+2\cos {\frac {30\pi }{41}}=x_{3}\\&2\cos {\frac {16\pi }{41}}+2\cos {\frac {20\pi }{41}}+2\cos {\frac {22\pi }{41}}+2\cos {\frac {34\pi }{41}}=x_{4}\\&2\cos {\frac {32\pi }{41}}+2\cos {\frac {40\pi }{41}}+2\cos {\frac {14\pi }{41}}+2\cos {\frac {38\pi }{41}}=x_{5}\\\end{aligned}}}