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.

As the ratio of the radii is $3\colon 4$ the number of revolutions made by the larger wheel is $$120000\times\frac{3}{4}= 90000\;.$$