Some rectangles are more fun than others, mathematically, especially for design. They are known as the **Root Rectangles** or the **Golden Section Series**. They are special because their proportions are such that the primary diagonals and reciprocals divide the rectangles into equal sections like fractals. **Fractal Geometry** is considered a recent discovery but the **Square Roots** and the elegance of their geometry have been understood for thousands of years.

Remember, we call the **Circle,** **Square** and **Triangle** primary because they are indivisible. They represent **Unity**, the whole, they are complete.

Let’s begin. A square has the proportions 1:1. The √1=1. Easy enough. However, the diagonal of a square happens to equal the √2 which is 1.414… (it’s an **irrational number** that continues on like **π**). We can construct a √2 rectangle by drawing a square and using it’s diagonal to swing a compass down (or up) to an adjacent side. *Diagram 1*

This new rectangle will have the proportions of 1:1.414. Further, we will find that it’s reciprocals will divide the parent rectangle into 2 equal child rectangles each of which has the exact same proportions as the parent 1:1.414.*

*Diagram 2*

**Note-** All rectangles that share the same diagonal are the same proportion.

The √2 has a binary subdivision by splitting the larger rectangle into 2 equal smaller, related, rectangles. As mentioned above, there are other rectangles that share similiar properties. Here’s a hint. They all relate. *Diagram 3.*

**Logarithmic spirals** can be formed by following the long side of each subdivision.* *Diagram 4*

About now you might be thinking this…

So you may not be interested in all this math. Fair enough, what do you think of this?

Now take a look at this…

Also, see how a young **Picasso use √2 the here…**

**The entire rectangle adheres to these subdivisions. The diagrams shown can be rotated or mirrored to the same effect.*