円周率の近似
π 2 = 2 × 2 × 4 × 4 × 6 × 6 ⋯ 1 × 3 × 3 × 5 × 5 × 7 × 7 ⋯ {\displaystyle {\frac {\pi }{2}}={\frac {2\times 2\times 4\times 4\times 6\times 6\cdots }{1\times 3\times 3\times 5\times 5\times 7\times 7\cdots }}}
π 4 = arctan  1 2 + arctan  1 5 + arctan  1 8 {\displaystyle {\frac {\pi }{4}}=\arctan {\frac {1}{2}}+\arctan {\frac {1}{5}}+\arctan {\frac {1}{8}}}