A Couple of Squares

And so we continue…

If we swing the diagonal of the √3 rectangle we make a √4 rectangle. The √4 = 2 so the ratio of the √4 is 1:2. Diagrams 1 & 2

Root-4-Construction
Diagram 1
Root-4-Origins
Diagram 2

The √4 rectangle can be divided into:

4) √4 rectangles- Diagram 3

R4-Rectangle
Diagram 3

(2) equal squares- Diagram 4

Diagram 4

A square centered on the √4 rectangle with flanking √4 rectangles on either side- Diagram 5

R4-Center-Square
Diagram 5

The √4 is the only other rational rectangle after the square as it is (2) squares.

Modern construction materials like masonry units, sheathing and wall board are based on the √4 rectangle.

The examples below show Da Vinci*, Uglow and Hockney using the √4 rectangle. Diagram 6

Diagram 6

We will look at each of these in more depth later…

* ‘The Last Supper’ has a surprising structure.