Golden Rectangle Template

This template helps you draw one of math's greatest phenomena, the golden rectangle.

The golden rectangle is a continuous, never-ending figure with sides in the ratio of Φ = [1+sqrt(5)]/2 =1.618… 

Relevant information:

The golden ratio allows the golden rectangle to be repeated within itself. 

How?: 

First, suppose we have a line segment, a, of unit length one. Now, add an additional smaller line segment to a. We will call it b. We want the ratio of a to b to be equal to the ratio of (a+b) to a. We need to find b. It is derived below: 

Now that we have derived Φ, suppose there is a square with side lengths of 1. Extending the length of this square by 0.618… creates a new figure. 

If we look at the inside rectangle of this figure, we see that when we multiple each side by Φ, we get back to the golden rectangle. This means that this smaller rectangle IS the golden rectangle as well! We can repeat this infinitely many times, creating smaller and smaller (or larger and larger) golden rectangles. 

I made this template for us to see this phenomenon up to a level of 6 iterations.

Note: drawing a continuous curve along specific corners of the golden rectangle and its iterations creates the golden spiral, something that appears in many parts of nature and pieces of art. 

When drawing with the template, make sure to use a sharp writing utensil for best results. A dull writing utensil does not provide good results.