円周率の近似
π 4 = 6 arctan  1 8 + 2 arctan  1 57 + arctan  1 239 {\displaystyle {\frac {\pi }{4}}=6\arctan {\frac {1}{8}}+2\arctan {\frac {1}{57}}+\arctan {\frac {1}{239}}}
π 4 = 44 arctan  1 57 + 7 arctan  1 239 − 12 arctan  1 682 + 24 arctan  1 12943 {\displaystyle {\frac {\pi }{4}}=44\arctan {\frac {1}{57}}+7\arctan {\frac {1}{239}}-12\arctan {\frac {1}{682}}+24\arctan {\frac {1}{12943}}}