2230.22 – The Golden Ratio
You see here a rectangle with a special shape. The shape has the property that if you make a square at the bottom and cut it off, the remaining rectangle is similar to the original rectangle. That is,
Find the ratio of to . This is a famous number, known as the golden ratio. Rectangles of this shape are frequently used in architecture.
We want , so we divide by :
We then invite the quadratic formula to the show:
We take the positive root:
Coincidentally, the ratio of .