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Rationals have finite CF and quadratic have periodic CF. CF in turn can be represented in terms of the modular group SL2(Z), e.g. using the standard generators S(z)=-1/z and T(z)=z+1. On the other hand constructible numbers in the sense of Gauss-Wantzel Theorem play an important role; is there something special about their CF in terms of S and T?

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