連分数
下線部はそれぞれの循環節。
2の平方根 2 = [ 1 ; 2 , 2 , 2 , 2 , 2 , 2 , ... ] = 1 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + 1 ⋯ {\displaystyle {\sqrt {2}}=[1;2,2,2,2,2,2,\dots ]=1+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{\cdots }}}}}}}}}}}}}}}
(2。循環節の長さは 1)
3の平方根 3 = [ 1 ; 1 , 2 , 1 , 2 , 1 , 2 , ... ] = 1 + 1 1 + 1 2 + 1 1 + 1 2 + 1 1 + 1 2 + 1 ⋯ {\displaystyle {\sqrt {3}}=[1;1,2,1,2,1,2,\dots ]=1+{\cfrac {1}{1+{\cfrac {1}{2+{\cfrac {1}{1+{\cfrac {1}{2+{\cfrac {1}{1+{\cfrac {1}{2+{\cfrac {1}{\cdots }}}}}}}}}}}}}}}