### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

$9 : 8$
$$\frac{b}{c} = \frac{a}{c} \times\frac{b}{a}= \frac{3}{4} \times\frac{3}{2} = \frac{9}{8}$$