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Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

There's a Limit

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

Euclid's Algorithm and Musical Intervals

Age 16 to 18
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.