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Good Approximations

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

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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?

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Not Continued Fractions

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

Golden Fractions

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The hints are written into the question. If you can do a little simple algebra, solve quadratic equations and argue through a proof by induction, then you can sail through this question.