Copyright © University of Cambridge. All rights reserved.

## 'Golden Thoughts' printed from http://nrich.maths.org/

Consider the following diagram:

Given that the areas of $A1$, $A2$ and $A3$ in the above diagram are equal, show that $${RX\over XS} = {RY\over YQ} = {{\sqrt{5}+ 1}\over 2}$$ so that the points $X$ and $Y$ divide the sides of the rectangle in the golden ratio.