September 1997
![Triangle in rectangle](/issue3/puzzle/triangle/dig2.gif)
If we label the distances AP, PB, CQ and QB as shown above then we can write three equations for the areas of the triangles as follows:
![Equations](/issue3/puzzle/triangle/eqn123.gif)
![Ratio](/issue3/puzzle/triangle/ratio.gif)
Notice that the two ratios are the same! If we call this ratio r then we can calculate a polynomial for r as follows:
![Polynomial](/issue3/puzzle/triangle/poly.gif)
Taking the positive root gives us the golden ratio:
![Phi](/issue3/puzzle/triangle/phi.gif)