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?
Which rational numbers cannot be written in the form x + 1/(y +
1/z) where x, y and z are integers?
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?