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Rationals Between...

What fractions can you find between the square roots of 65 and 67?

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?


Age 14 to 16
Challenge Level

In order to maximise the reciprocals we want to make $p$, $q$ and $r$ as small as possible. What happens when $p\geq 3$? Investigate values for $p=2$.