# Are continued fractions ever of use in physics? [closed]

Do you know of any instance when a continued fraction is of help or necessary do describe a natural phenomenon?

• This post (v2) seems like a list question. – Qmechanic Apr 8 '17 at 6:18
• You may interest in the example here – Ng Chung Tak Apr 8 '17 at 9:54
• One more use: method of continued fractions in quantum scattering theory. – Ruslan Apr 8 '17 at 14:39

If you want to study angular momentum, then you want to study the representation theory of $SU(2)$. This will force you to study Clebsch-Gordan coefficients, Wigner symbols, Racah symbols, etc. Locating the zeros of such symbols often requires solving one or more Pell equations (i.e. Diophantine equations of the form $X^2-nY^2=1$). The solutions to $X^2-nY^2=1$ form a free abelian group of rank 1, so to find all solutions, it suffices to find a generator of that group. That solution can be found as a convergent of the continued fraction for $\sqrt{n}$.