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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?

The Genes of Gilgamesh

Age 14 to 16 Challenge Level:
* Do you think that it is possible to make (GGM)?
* What other ratios (e.g. GGGGMM) would be equivalent to (GGM)?
* What possible fractions would be within 1% of (GGM)?

Can a fraction of one third ever be equal to a power of one half?