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?
Keep constructing triangles in the incircle of the previous triangle. What happens?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =