九十七角形
( x 1 + x 9 ) , ( x 1 − x 9 ) 2 {\displaystyle (x_{1}+x_{9}),\quad (x_{1}-x_{9})^{2}} のように和、差の二乗を計算すると
x 1 = − 1 + 97 2 − 97 − 7857 2 2 + 97 − 2425 2 + 5141 − 25927033 2 2 2 − 97 + 4753 2 − 1649 + 2705233 2 2 + 2037 + 3841297 2 − 3488605 + 12162451874697 2 2 2 2 = − 1 + 97 2 − 97 − 9 97 2 2 + 97 − 5 97 2 + 5141 − 517 97 2 2 2 − 97 + 7 97 2 − 1649 + 167 97 2 2 + 2037 + 199 97 2 − 3488605 + 354099 97 2 2 2 2 {\displaystyle {\begin{aligned}x_{1}=&{\frac {{\frac {{\frac {{\frac {-1+{\sqrt {97}}}{2}}-{\sqrt {\frac {97-{\sqrt {7857}}}{2}}}}{2}}+{\sqrt {\frac {{\frac {97-{\sqrt {2425}}}{2}}+{\sqrt {\frac {5141-{\sqrt {25927033}}}{2}}}}{2}}}}{2}}-{\sqrt {\frac {{\frac {{\frac {97+{\sqrt {4753}}}{2}}-{\sqrt {\frac {1649+{\sqrt {2705233}}}{2}}}}{2}}+{\sqrt {\frac {{\frac {2037+{\sqrt {3841297}}}{2}}-{\sqrt {\frac {3488605+{\sqrt {12162451874697}}}{2}}}}{2}}}}{2}}}}{2}}\\=&{\frac {{\frac {{\frac {{\frac {-1+{\sqrt {97}}}{2}}-{\sqrt {\frac {97-9{\sqrt {97}}}{2}}}}{2}}+{\sqrt {\frac {{\frac {97-5{\sqrt {97}}}{2}}+{\sqrt {\frac {5141-517{\sqrt {97}}}{2}}}}{2}}}}{2}}-{\sqrt {\frac {{\frac {{\frac {97+7{\sqrt {97}}}{2}}-{\sqrt {\frac {1649+167{\sqrt {97}}}{2}}}}{2}}+{\sqrt {\frac {{\frac {2037+199{\sqrt {97}}}{2}}-{\sqrt {\frac {3488605+354099{\sqrt {97}}}{2}}}}{2}}}}{2}}}}{2}}\\\end{aligned}}}