Stage: 5 Challenge Level: 
See the problem Tuning and Ratio in which you have to find a decimal approximation for this ratio using logarithms. Here you must find an approximation in the form of a ratio of two integers without using logarithms.
You could use the same method as given for finding rational approximations to $\pi$ in the article Approximations, Euclid's Algorithm and Continued Fractions.
Fibonacci sequence. Music. Quadratic equations. Euclid's algorithm. Limits. Limits of Sequences. Diophantine equations. Continued fractions. Calculating with fractions. Rational and irrational numbers.
Published November 2006,December 2006.
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