九十六角形
{\displaystyle {\begin{aligned}S=&24a^{2}\cot {\frac {\pi }{96}}\\=&24a^{2}\left(2+{\sqrt {3}}+{\sqrt {2}}+{\sqrt {6}}+{\sqrt {16+8{\sqrt {3}}+2{\sqrt {104+60{\sqrt {3}}}}}}+{\sqrt {32+16{\sqrt {3}}+4{\sqrt {104+60{\sqrt {3}}}}+2{\sqrt {848+488{\sqrt {3}}+2(31+16{\sqrt {3}}){\sqrt {104+60{\sqrt {3}}}}}}}}\right)\\=&24a^{2}\left(2+{\sqrt {3}}+{\sqrt {2}}+{\sqrt {6}}+{\sqrt {16+8{\sqrt {3}}+2{\sqrt {104+60{\sqrt {3}}}}}}+{\sqrt {32+16{\sqrt {3}}+4{\sqrt {104+60{\sqrt {3}}}}+2{\sqrt {848+488{\sqrt {3}}+2{\sqrt {358376+206908{\sqrt {3}}}}}}}}\right).\end{aligned}}}
cos  ( 2 π / 96 ) {\displaystyle \cos(2\pi /96)} を有理数と平方根で表すことが可能である。
cos  2 π 96 = cos  π 48 = cos  ( 3.75 ∘ ) = 1 2 2 + 2 + 2 + 3 {\displaystyle \cos {\frac {2\pi }{96}}=\cos {\frac {\pi }{48}}=\cos \left(3.75^{\circ }\right)={\frac {1}{2}}{\sqrt {2+{\sqrt {2+{\sqrt {2+{\sqrt {3}}}}}}}}}